{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    }
   },
   "outputs": [
    {
     "data": {
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sfXpb\n+vwdcUwkwXEESqmpbVY59lAwrfZJDmEdB+8Bu3nYevoHCl4l+IkuoNjL6ArXOrsOJbqUmrMpUkD/\nAHk3Pr0xh79Lnjxwl1H3z5WaX1JFjYI+0l2243TuO/wJxXnCl9mKVjJrGoqqpppouXHTsSgAOFVH\nGy9+wiCngPO++/PDF40ZBDtFnTykWKYzSrX2ALTAHrxbGvZ/k0fNPjAtpZQp1U5mJuASpTKUsaSd\njykgfyOLM4SrEXdqCNycKlO5sDuXeKmN3MO3rhIphEdjsQT2IiI+nftwzTvEeHljJxortkuU6gxY\naUHYXRTW0gW+JvY882PGPn/x9plUi+KqKbGK0RqWilMBAuBZEWOsgAbWuSLcc88YG+Cr66xjZMux\nhVNt1b7KnSARHpORugg1KcPAAG0jB27emh7cKVQyZNqnh1lyoshaAMqsOqCQRYvJekk7D/6l9z62\nxsXjMmmZhi+Gcd9SEyouUaRGcCrBSVLKnSk9d9YO+99yN8Fyjsz5ptlnuZlSmPHqMYE+hDqAzVuL\njp8dugHIG12EOoOwhw+eCFcpmU/DCi02oLQh5TE2a6XNisvy3rrJvuVBAAPB0/EYxH+0ZT6hlSk5\nLoVNSsNSoK6mNIIT/eH/AC9exsdYaCTxcDbi2HbGlsVxHnK/Q75TTCQrNUcpdRvugoDue+8G9BsS\nm6TD+G/fhEpkabXKdW65QvMQ3Izbmd1K2rgKaKYKUm6eRqbJAAuOBg5m2lxcyeAfhsiaEmfBqlfa\ndCx72lxulkA3ttdJOwvcEdTieZJmS5vlIAIcQFSmvXhnJyCAmKWUQXKQdh6GBDpIA/MR9uNH/s4z\nW41LzB9urSqYqvVaOFPEavJYlpUhPvXIA8w/M8dDjGeqZN8NclRpkNCkt5np4YCWxZKjAlsugnpd\nJcJ68gC2ByxcvsY5qx24kxP9my8fZWionH7g9DJAQ3vsIlOBTD1aHiDNYCs65lqWXrl0Uyh6i1uC\ntqfUEKB09dKhexuPTjDh4ZuDOPgBn6nVIBMqNPy/LZS4LEpVJlNrKQSNrG1x1v15OecrdGXOolr0\nIJVZYkrCyjcERKY5CM3pBVOGu4aBQNjvsAj7cAfCudOr/iXWmsxrKm6bBhqjIeJKQZaJzKwArgEN\ngepIGwGFDKeXnMiUCoZpjNhuMhqfAfWNgtM6BLbSkkc+8Bbc72ttbAM+yLn/ALV1/wAR+PrT7Jof\nZj/0f0xjf+kdP+yV9D/045DAQ7m7fWTH6UJEuzCICJQE59b3vXYw9vkPoHHy/GmMtZUkUl0Dzooc\nQ2Cd9grSAObnp2x/T6aRJy6w+ybvwVhSCLkqQkggDra1x8frgkswGh2BF2I6ZyKR/iCH7oiYxR77\nDWwNoR3v3Dtxk6CvNNJnU65L0RZSE7lQSAQNhc9Pp644kyU5lobZJPtENTZF7agAON97WBB72G18\nDqxPviXo5WgiVGVIZQAAdAJj6ENa8/e2Ude/YR9dHydAZdybKgTAn2mCkpQT94AIULb9bjsdz3OD\nry3v0TjTEnW7Tnm0qF9Vmxe477c/yscTnFyiNcsslESIAmjJt1F0vidiiJhERAOrQbHvsfn8+EDN\ncqTVMtrjsFS1QV+SUpNyNJuk23sLbfO2/TjOCvt+iUitxTrfguMtrKTdQASLXIueeCLX42xBXDha\nOslkgWpzC2cKuF00yj90wLCJT9Jd6Ht30Ab+fDhRqU1Wckxp7gBlwGUIXq3UC2NSeLkEG979MMlV\nnJTTMt1xwXKVMRnnDykoCSjUe/Q34+NsFTD6DR9SLZX3pS/WWRXRUwN0gJQVRUEohvvruX1/5pHi\nBXJTkOjFtSlNoXFXtfYtOJSoG3pf+PY4X/EAus5yy1mSKSG5SYylKSdjoUlKrkbd+b8XPcDCOmpB\nWmSleKY50Wn1yP0AmEAAgn6NgGu+hLrYe4+nDpVaAymLSczoCQsOQ5ZVbfVrTq37kpUL3w5VKREg\n59pExYSlVQ9mloP7ylgBfO43uCfUHbpYpuxjJ7l0O4AE/rZK6sQTCAdYKtO3f1AdE779tB3DupZy\nzVIk5poMRV9LFeiFViSC28NJNth1G/AvydrZZHjyaF49uy0lYZkVVKiBeym5PO1iNyq/c35OBNKW\n2TdYySaHUOZv9lIFEOoddJUkw8a9OkBDXj599uFayo1RcwUCuISkLRWWVhY2OoqKhf1Ivfj44fKA\nuA14rS4I0JkJnSFAG176lkeo+9vY/MYs1lSHh1sEv3zYEwXNXWLpMwAHUKqiTY4h6DsROID8+4dx\n7rdUzg9Xc35OpGk2/SRDbgJvsEyGyeTtwQdsYt4VQplK8bDIUpelVXntLSb2CCqQNiTtbb5E24wL\n1ciSsLjUjA6qpEG0MRscBEQDQNSpAHnXcRHsGv8AC3nfI6Itey9P0JPmV6M8DYH3kvpfAIt0037W\n2vjQcqppeYfE6W0gNrkqnuvCwBIUh9SyT8ADvzvvYWtYeKpUP/Q80eEMBVlKei7E+w7KDFFV79g0\nO9gPf+WuJfEnxDTPhmhtjU9MrUKIE8myqmykpA5Nxva3A9N8S8mojxwem3UWms0uhKLGxR9oqAvz\nsemwGBxhHKD+m4rjokyhilatlzlAwjopVllVx868gfqHzryPkeBni/kaQuDNnJStKHfZ2za46NNA\nEXNuCngX4366x4hQ6TmnxclAKbU89NbZIBBKlNIQxbqdQKe3oDwQTsVUxK6Vh/cvigY9hkpt91AI\nCIiaQdFAwiHcd9HYA9u/y1eoZ2pVDyQmlPKQhdPy7FiBtVh76KY2kJA26nfv05xh3jgKrA8TotJj\nBQj0tmkRykEgJS3EjKKQNgOTtbk2G4vhDy5ZCUx7IZRiHhhFP9u5YUxMIBv6si3a7L4+7/VCGw89\n/XzklZy/U5GRqBUIXmNt/ovGcVoCgP1wdkgm2x/1gO/fodjrvjnTYGY/9HRJQX28o0hlaTa+pepw\nhQO+o679ztt3nTZq4yzcp+5Mh2kgkxhDmTHf32RVVugdf2frQj/5tfPjU/A2XTaJ4YUqFUFNiU6i\ndOfLlgpS5Eh33lA9SEJ37D0xhvjp7fkylZQy9FCyhxhyohKQdI9pWhsm3QkMgX52vcdVGGLWeg5d\nyTXplQCoKRtWcIfEMHSBzBKnEwb/ALZDl7/r27cITS5yabOqlA1Bl/MeZlAtcFHtEcIVcbAXSbHD\nbn6ix80eCPhfJfSlUtl2utPJUBqILkEJSeSCkp26HfpiZZkkk8ky9TWrwgovWHUiLlRPQiQkggdM\npfujsoHBEddw2IeeHf8As+vJqEDMEyvELlvVadD1PbqLUOWpTY9+xIHmXFyQAdsZHXkS/DTJThbS\npqNmKGyhLaQQHFwZSXOByR5x/Ha9sQKtSj2o5fpradMYWMvF2BA3xhHo6kW7U6X7w62VQO3YdAIa\n78V8yJTR855iqNE3V7BQyoNb6iJVQQ4DpHbftcb83w3ZKWjOvgHnRl1ATIh1ShvNgj3i265MbXYn\ne1u3Xbti6v7R1n+23/RP/HgV/pBzH/s3Pof+jHzl/o7Y/dP1V/THCJnFJqxaUgHZ01TN19u+gHYj\nvyHoYPTyHpvhYqtTWiuKYST7NMXdJB21K252GxuDz9DYffUKYqM7Ipqzdla/1RJ41EkcnexuO9iO\nb7N11nySteEoCP1uONow7AB6RL0mMHroR0bx6j+IlcqUY0jMXnuJHs0617iyLqJNyP8AOwvfBPLz\nQjznYxUAzJSoBP7qjqI+huLgdtxziEMm7l2nFzgAYxmol6zdx0AaEd9x7bD8AA3fXDDXJLVHqUmM\nwQhuYkEAGwJIII2AG1+3PFr4NUiZZNWoEuwK1q8sG3vJKTpUO+xAFuwsb2xP8hvUUWsFZWJilVIi\nCawk7CHUUuwNodh3EQ7+3fhEydEU/XqpSZd/JlOakah7tzcAi+3PYbdd8fsoIcLFWoUi5CVLU0FH\na6SSkp5G3oNuu+IJDOyr3aNknX3kHxUkFTD42bQefGxAQ1v8+HdZXQIVXpCbaSFrQngFJSb7b8X+\nHPXBmQU1bJE6A2f7zAkOOJSfvJLRv/6SOwPTE3mXylGusik1OJWsy2ROUAHRTCCQgb5dyj3DvvXf\nvseEPL1NTmqkvMupCnYT79gRchJUD2Ft9x6HYdMRxHE1zJlPkvgKkUlxSVrULlKdQG999lA9du3T\nGeIY9rOPLbGuQ/rBXVdogOv3VB7DrwIfe1v5eBDsLFmOsqg5QbgqvdpBZsedTR1WFuDYG3B339KP\nibIeQjJldiqJDKGmnFJJP3Sk2JF+LHvt13udULa3cNWLFTjKG+G2XlGgJ67dKp1BTAN+A0YBANaH\nWuAcjLoq0Sn5kQm6kIiSNfNlMaNR2v8Au3v63tvYMtdjxXcx5er50gzWoD2sm13GwgL3OxII4t3t\nvgh12ts53Bqj0uhdJQr5Ee4CYFmqaoa9fAAHsPb32HB3PGbELNLiagHG6pTHDsNkLUhJPzvf+XUZ\ntVX5dG8fWZwJEWRUYiyL2BbkhAJFiNjffob29MROWyC9fYsTiFVTCl9koNzFEe3SmiQo+ohoBKI6\n8eQEOK8jKP2VmKiV/SbNVmO+hRG3vuEgg7WJSq3rfGgUeDAi+KzqE6EyDPecQNgSVKWQbEjc6um3\nY4M2SKrHlws+lG2vijAMnhBDQ7FUjc4gOgHz1Dr0D04sZgza3WcxZTpbZ1FWYUNrHVNm32xxbqB6\n272xjnhSmdTvG91x1avKcqtQYsq/ujU+E2Hba1+DsbjrHf6UH8bjZKKOscE0oQGZ9iOgL9TBHpAf\nHYRAAAP4duAebckqj5hoU9xu6F16LIF72OiUl7e4tf3bnrbrtu/5fptNrHiZKLWhT32k8+Ei1yUy\nC4dr/eABO/x35JO/YJqjicz9JUoKjVive2v3vswFhANevqPz7jr0a/EDPEOfBbpKAFvS6xBiJTtc\nBVRabNvXbjrvsBvjHqc/UV+OHtCypUZOaFoA3uUmolI1cbbbX3564b8EZUWqmK4uLcG0LZBwYvUP\ncoLLrKjv72tD8QRD8Q323tG8XcrTizMkNlxLb5Ybsm4SfcbZsLgWv92/a/XjT/EaiQMy+LE1bakK\nW9JZQoDSSS0020LeoKLbbi3xw9Y8p69piJW2IGDpnpadfEEDdjCaRdFE467DvpDvofQfQA42idXq\nPTMht019TaTAy1FjaFaQQpFLbGkA2OrXvv3+GMf8ZqhUqf4kQKQyHCxTI1Gj7EgNoRDilSQOARqJ\nIHW43uCX7luyCSpt8iRMopoyN4mRTExg/dQI3biQNiHYPhdh152PrxjFahVVjKVFk04uIZVlqK4r\nSSBqcS8/ckW5Cxfa9j1vjSvHigRcwTshPNpQpz9FKO2sWudawp0n/iPmb+nptjByV1eci2q2ROyt\n1E4mNOdMexjMWZh6REBABMArG2AeN68DxsPhEzT4/hlRGahoVKfYmTXysJuXJUhZWTffcIA336jG\nUeME6Zk2h5Py4kL0IjvzUoAsLypAuoD18pIF/wAbXEiwlafsTJGQq9OnHSbStrtwWHwZROSE4h1D\nsBOUxREfOyh8uM4iTJdGpsqbRiosP1/Mtyi+kpblNJQo2NjwU9Lc9yGDxOoLOZvB/wAMZ60AvLFY\nQ+Lb7PRAi4tcFJSQPUn1xIc2PELBO0p7Xek7mFPLguZAe6ZHiRCAAiURAN/B6tj7B6iGnPwTUMzx\ncw1Ste9IenOwR5m/uwpLhTYHfl0gdbc7HfMHHn/DjJFQYCC1ErsaGUpsQHHIUlargbA7PWJ7Hc83\ni/1yz/7Vf/iN/jxsH6MUP/ZM/RvGNfp4j9xX1H/Rij7ybTh1RamEoJLAdI5d9hAxdAYPcdD+Q/gO\n/maFSV1eO1KsfMYWCb/eBCtx8Pn34x9rLAcWHwdJ91YUNwFA3IO3Fx36WvgVomWdTL1iPUZNx1AX\nYiJTAbsA69NlEPzDwA8aTNUyijMvjSl+IEknYKsnk356b9t8G3XFMCDVGraUrQJCd/dN91fXf59c\nFKnt0W7B3DPgIUyqagJAYPvCYAMUQKBtDvuUwa8h31rjJ8zS3qh7NNYUVKjuo1EH9m4JvuSeoPTc\n45rD5FQi1WPaxKA6UjYpJSbm23p88C+ekF1m8hCGExvhG/qSiIiPUURDQF8j1a7aAfPYONCp1LQ2\nxArzOzg0B61gRuDcW5IPf1w2w5TUKrU6WqyWp3uqULAXVYe92+Z6HqBh/jowjylllGwgD6LUSOIF\nHZg+EJDDrQ9QD0iG+/YOkQ8913M1XC8wxdf+rlp8lZ2sokFO/HHP8+p/RJH2bmqTBcv7FVg4Ug7N\nlToKTa+xN9+vXfDNcbEWcdVx+ocoHIui1VOc2hE3YhSdxABEwiJSlDuYRAAAR4K5SgHLtQlFQszK\nQpYB+6rWOfU8EWufntg7QoAjxMw0fkLjvvNpAPFtRVbsBZV7DTvfqcTiKXUodrjZEBErSWjlSHMG\nwIcRADp7Hv8A6o6D8PQd8K1baTXFVSA1YluT5rYHQK2Vba2/NyOh24wuwAcx5Pl05665VImJ0gm6\nkpSog2vvwAT1t88IIZmnZLvaWqIhp0QjxIoeBMIGMfp/Iw7+Qb7cNtCfTTcnuU+Vs400+0ArYj3f\nc+BulO3qBjzPEl+HkzLM9rUXKfLSy4U8hIIFj23A2vcYmVOtpq3XrTTnQj/UP5RJMhhAOlNyQRDQ\ne2jD29/A8ZvVqO9WhCqbJKkpajrVa9tcZYtxyRoFyNrC2+LeYYLdVqWV8zoteTDp61r7uM6Qbnv7\nu/J+GEMPVQmcTOJNLZjpR0gAgHcQO1FUBKIa7D0gAh/Dv341XMtfjmkQ2FFPmtyaYq3XdTYUe9ub\n/wARbCxX6pJpXjvTHUlQiPyqepSrm1n0tgnpsSevr83OWyOu/wATJQih9gMI2aCOx7gkkmAAOx1o\nAIGt+RDQ+3CGrLLkLNNIrKgfLZrLMkXBIst65IPqFW6EA/R4pVDiw/FJ19ISl01F54Db9ta1CwHH\n3j+SDiT5Cp6bXFLmVQMAmCKZui6EPvFW+rj09u/YFA/Dv379nLM2ZY1Uq2WYDSgpxVbSggWumzb4\nHxuQPpf4ZR4Uy50bxtfEgn2ZdRqTIJvynz7Ej5Dt8hhyXym4b40CJUVDQwH1AwiI7APqPwCh3Ht/\nZ36gGt8IVbym8zmahy3Ur8r7eiSSkg6VBExDyjbe9tJO/r2Aw70CgwZ/iRIkMhKnUVVcqyebplea\nSflvfji/G7onQ1mOMzyaJwAQroPQ12EAGP8AjCAa0Ow7j38Dr37aB4i5pps+EzTkaFPSaxBjJSLE\n3VOQg/K223fjoM1o9Smu+NoL2oxhmJbRUSSFJM4oAIvsLC29/n1kmCcnI1/GETHuhATtknehEwbH\n4zpwtsQ2I/6+/wA/YOMy8U6PVAiYppbiGXksM6Rq0gKZbZNrcAgEeh26YePEzLEfMHinNfaCSp59\nhJAAVYtMNN2HN90EbftDtvhqqFckJhjNWRmBgRmpaaflEm/vmVkHICPYQD0AN+wAHoPG3z5NHh5A\nagvFkLhZbisHUU6gpFNbtzyST67npjOPFeuToHiLSaMkuFqmx6NEHJCEIiRrg8AWuSQbWvzbEs5c\nLu1jYu5MpZQPjJ26U6TqDsfhokRbgn38AUUh157bDxxkddeq1Jy7SjTitLAoEZWlOoJBWHHb7bDV\nrHxt3vh58fsssVqsZRdaQlVsuUtKkhIP6xYW6pW9xdRXv8jthlkHDqcyfbp+DE31ZVKHZmUTEekR\nZsRNoRL4Hawj535347aX4XUyE54a0b7TKVSpQqc10rtcKlzHFK+9v+yN7HoR2wieJ1TfyplbJWXX\nE2DLEqShHrJlKvYHYizYva/wxMMNWZNa73aEnT7OzbQqrcFh7gKxXhlgL1m2GwEvj09O/CRS6k9l\nemPvU4KUw/Wq/fR90+XJbSg7dDYi4/paz4q5aZr/AIW+HdQQ2AZKKl5wSP3VsBBNv+Ej62xaH63X\nv7Tf/jL/AI8CP9KlY/3vof64+av9GzX/AMOfof8ApxxLmZNWYbpOUjiKiB+lTQ9xABHpEdeofn2/\nhqFNZao7jjDgs24Cd9hudzc2vf4fQ74+uYLQLj0Z0aUuJAH+6oAHb0sL7jjbriTQrE51GUkAfe6S\nlP28HLoQ38hANBv04V6vUtD78K90LJ0i5spKrj8L9eDb0xIl3REk09w3UhRsD+2ncBXYbWNrXuOe\ncXIxJJY6aVTIo32YqDRtZ3mP4aAhrFYDQ6MtaK2rbrdFEsKjBw1l4HHis82rETcbYV5EMWrKUPHj\nLtFVHDhj7kSnxXV1aDUjHUzMchojsvu6VOONKkSBrSlSXURA4GUPvgtosvy0uJVcpznMBrj8ijt0\nmPUnXaW1WpUqVDie0KjwJqKdTnjEDyHI0qsJiLnSKZT/ACpDrjkcPezLQEIdmkax5Q2E3ZLJESMM\no8/ZnKcHXq5DZEKxmrQD2yR8XJWpvcJa3NGkM0/YmwzldxzS52NjrVKsqlMWRmyyOjbolNHTXFUe\nkU2dESUgNtTUsMIlpQ44CspDiH3HgGv1Di2o7DgDziY61pTK85OBjsrxFq1IgRH2ZVotToMyVPkU\ncuxqcpiBIfZpy6bGpy3pLiqtCiTK3VIz79OjuVKLCecoiqdILi6mWfD1fw9X4O9zFGmUnWLICvjS\npGXfx8mtecYDzfXdujY42DcRc/FV2ZnbniJlFP0pVija1ZxCux75RWPmSRmeRVUytUiI4+uLJeis\nshyGtxxDom0r9JpDYfQytp9thx6ZTShaXEJkeaGUqJS6GylRj5mqNedqtIjVeK5HzHMnLrDEZl5h\nFIr48MqQtUGRMbkwpE6LFpWZnZDCozy6cmIuc+yEvxjJXSGO+UuvsSyMe7qMJE2yNyc+pU3GZBtz\nmfslff3PmPpMhHSzFzNPGzOhsoWuY0ialKhHtH07MfaLR5KTi7mdKz0eomhR6ZFkKcYZSWpKWHEP\nu+Y4ytVQjlC7rJDOluOhpR95agUqWsldv36TeJT1ZiuvIqUp+KvLsSrxZFGpqIMOcxRsj1hh5h5u\nK2Xaw9LnVyTUI5dcaiMFlbUeIhuIXJC/q3J/kOnW+eaNauygqjBSczZXUHab6tIY9qsDfFa5G2Ki\nldzMoM1LS0EZm/tbOwftGoQZCCkIeHZDMpNTJlHp2XxmCfLZbjpbdY85/RImL9mZadcbbfiJcdWl\n1b4LSpiXi9p1MrZbaD1jPTp/ifluvw6cp2ouzK5LjRYLMym0VEevVKdQxPkQawW4kcRI0ad5rFMd\ngfZ4PkTWZUtwRVuCvltaYTqcTDT9cTxtH3yRvJY1Vrjm6z1qbiwPNZZbzzACSVhn2amP42mx+EJa\nk2cVPtSfsdkuSbqSeOk5mFrHmfY8BulTG6eYrcwrbdS3GfW6SA5MEhJQpbiRGQymAph0AKcddfBW\nshaGmagyM3V9FdoFTcrsikU6muSh9u0qFT3ESQxlp2A8PZ4MN9Nbk1J/NserwADFiQYNLU0wygRp\nVQq1Y24vb/OosTAJXrMj0oJ9wMYBApxAA9wMPz7D39eA/h8ltygPRpgGttbzadQ3AUFEc+pHGxvj\nQqnMcgeHFMlm4cpc0Mk8FLd9ueB1+Jt8Z7jiwoxdMtNYfH6VGzt+kmmbv/Vu2wGAAAfAdRx7j28+\nO3CHmaPKkyYy2Lqa0N6wL2C47xGr1ICBb/PFTMcIViq5UzOyNRkwqc4tY6OsOAEk7b+7uLgnnjA9\nZV1eQx4tIpdRiJMXphAB2IfVjrFH3D7oFD5+PQONhrU2KaFFUdIfaep6gdgoFRbCrnnck39RjitZ\nhdpfjdSY9yGZb1PJJ+4Q+hAN9upNzzbjpgjT+QySWJUIk5wFRSFYtVBES+USIhrQd97IG/w7+usr\nYosljN1KqDtywzWUPpFiQAp1W9ybAWV6c7DrhgomXWoPie9LQNKhUZTyQBvdwum4PJFlX67nDfkK\nprRtAXkSdyAiyOPbQdC5kQDQjrto4APYN79eNLzJV4c6dl6M1oLyqgoAAgkaGXVb23F1IuOnB6YQ\nvCOrS1eME5iRr8ov1NCSq+kqbS8U87CwTdPfm18EJ1kwCYyNFnMAKHrpmIDsO3+gfC8CIDv0+fft\nvjJ6rl+T+lVGcd1mOquxX1JN7FKJrbt9+m1/T4g4aKFlqPK8RHJrRBLdXVKVbkkSw4enHyJPr0i7\nepyMbj8ZNPZUywgPCgA+Ci0BXYgAhr1H3DYiPrxrPiJVKVLgsxUFsvu1SJHQE2KrmSls9b2tsOnH\nrhQo1bly/Gr2d9S1MqrzrB1G6Sn2pSABzb3Raw26c74LuFsgsY3F0Q0eiAKoIOgMJh0JhVcrqgbv\nv7oif17fr3x7xHZqzapbDK1iO/5LOkE20lhDZHQfAdNhbrgz4k5VRWPFCdIZCVFyQztYHT5TLKAk\ndbDRyNr/ACwKanGyarWZl2RVAbyUtMPg+GA9JxUfudiAh57FAA7aAPTYaDdq7EpTeSksOlvzYlAj\no1EpuFNwGyLj43GF7xJzRIi+INNo6yVNwmaXDSk7gIRFjbE9Nyb/AD22wSeXizMTRttLKmILn9pH\nQAZXQm+EgggiQNj56RTMGu38B4yisVWpUChUlmDrSwmjNkhHALi3XDYA9Qobj487YYPH7K7dTq2V\nS00FtoocMaRY2cdW46rYX5Kxt/MDEVkH64ZRuUrCCPwFixLcTJb6RFuwIY3jWxE6ptgOvAAHDx4f\nURipeHdKeqBBkSTVJR12NjImvKHPokdfx5BZ9qpy7k3I1BkoA8mPLeCVW2D01aQm1thZsW2NuvW8\ng/aef/2q36m4TP0ahf8A0/x/rhR+1oP+xH/J/hil8IwOi5cIK/eRVMIbHuBREREo7+fgfQfH4M1Y\nqRkxUOtH9Y1ubHcpFr9+Ph/TGhy3G2wxITsvSNVuVDck2B54/HpfBIarosEioHECFOAFD/dPrRRD\nehAPb8hHfCoppyohD6QS42Rc2N9Nxfm3+FrYBy1q9oD6TcK35sFDkg9fyBgey0uo4VfR5jj0nHqK\nAGHZVCbADa2Ib9BH+7jR6fAbYZjzk2DiAkOGw3HPTc27dO5xO04Iz8aQB+rdUElXQFROx9Cdhe3a\n1zbDnWI87hmm6ARBZoIiICJtiQR7j22I+A342JQ86HhezRVAp1NvurslVienG3+92vue2CRcTT5z\njWwjz0JWRyEvAc2494E787/RbeZMruOauEz9LhoYEVSgYQNodfe870OxANediHrxXyhEMWpr8xJM\naWNab/dOoWV2sRe+/Tfi9r9CbDK50BX3H0Lcav8A7wPF+xsSefXDVS3rlGabJyLhyszcIHaNiOF1\n1UWyK6izgUWiapzJtUTOnK7k6KBU0jOXLhwYhll1Tnu5wCkR34rKlWaBW2kqvZIJWABe1tySBbe5\nPJvI4oVGguJCG0zKbIUtxSW0IccWzpQlxwpSFOqDSENpWsqUG20IB0oQA3TczNRSNmpzSXlW8HKO\nEHr6IbyT5CJkl49Y6scvIxiTgrGQWj1FjqMFnjddRkoqodsZIxzCMuXWVzaQiQFrStsIU62laghw\ntXKVLQFBC1I94pK0koJOg84bA7ELVAzI5HjqlRdMX2pbDS5EZuQlLb6WZC0F5lDwADyW1oDoCQ4F\nAWElVOV9jxhKIj/p0K7TE4gI9YdHgR86HuIb9d9xEPK/NmKXXmYrxKmnmwgdQQo7g3569B02xUgN\nph55mt2/utaiqHoSsAg2O2xAPHfjCOnTQmvME9dmAyT1uVkoY+9CC2xTAfTYiIh6enbe+DlTjqok\nJ9yONIUgvAJtvptqFgdtj3vjmuRm5uXcz0EAeZEcEpCBudKTuQm5JHwtb64frimqwuk02ZCJUnrJ\nJ6BSiIAIlKCZx0HoG/P/AF4pZLbZrMN8PgFaH3UoJH7xKki1u5HWw9DgZCl+yeHVPku2K6VLMfUr\nkNlRUPpv87YnGM5NsbHdhhnYlBZovKoAU+t9DpEypdfiKmvzDxvhazVKltSm4jZV5J8g2F7BTD1j\nf5Iv8u2+BWa4aanmXKmZmN/aIlMfCwLgLZcSlVzY8aduu3fAmNGvFaMV4QDCimyVU3/qgCJzkN6g\nPYSeQ+W9calUUxFUqNISEpfbehkq/auooJ36bqvv3t3wbn5lMDxoptNUbNy341wfu/3hsAfHdXb4\nAXwYrpdW0ti9tHgICsuwikzhsP3kjNRNrvsd9Aj4EA4y+mQpac3Up+QVFhmpqULk2CVl1Ive21l/\nzF+suVMu/ZviNLmJFtMmorSQNz5qJAtvtb3uTz19YfeoJ7FVA7rZgTAWqY632KscpQD00AgPj8vP\nGjZjkQpVSoSGAjzlSHVDTYE6GisEgDopH4X+K94PV1+Z4mVONIKvLSmolOrca2tagUk8kaPwwWHV\n8bDi48cIAC560LQN+QH6h8LuAj5EP477eB4yiqU2a5mmlJeWr2dVdjPEEm2lE1Dh24sNz27YLULL\naHPEhc9ohQbrRkk9R/e9ZPp24tY2AwPQjJSHopniZVCIIxn1kmgHpApkAVA3b02YRD5j541XPaaX\nJjxGm/L852pR2BuCpV3NJHW5t27fUdQa89VPGJUKQSptVVeZVqB+6l5aBvwbAWsCb27XODViK1Ri\nONopJ4YgOEm7oVBHuY5lHDhQRAR0ICImEdj37iHcB4yzxBl1VszIbSnBGeQ0wBc2CSw2gA/ACw6W\nI7Yg8RMsKqPiZPlMoCgqSyUG33A2y0m224tp36/AjAXqH2i2QmHjIpyt30pKOwEgGAv3nq5Q1r7u\ngAgAHt4HsGh1qu0aArKLRcKfOjUSODq07FMRC7b78qO/N++JfEXM6ms8UykPDUIjNMi2VfgR2Dfj\nYEqO2w54vgnYLk2Mo2tTiT6DuxnTkAVP3vhotUUg7iI9gEo77hodfhwhz67Ny3QaXEi6ksopZKdP\nCVOOurOwtc++N/jucSePWXEzallVttGppqkskBN9luvuO9j0WBvv9cG3df8Adt+ocZH+lFV/fe/5\nlYzr9En/APYuf8hxz5K7TSTOY2gMTQHEB772PSb+HcfQR1xsbUVwSSjctrJIB4Nz7wueduBbf6YZ\nC95zflnmx0XtcK6i29ufXa2GOYnjLNepIw9SZgIoAD30Ah0m0A+B9/HpvhnpVMTFeUlaQUrBUL8f\nC/pva+1jzttEyyp1RZXtcHTvslW17dr87n64Z2wmdu2zzuYVOkqgj662Ud997EP17cEZcpMZpyKC\nANKtHAsDxa/x72v8cXY8cqjSY7wstu+m/IUDqSpO/ANj/O2CvGCnEkE/b4By9RhEP/VmDY9u29Ds\ndeddtcZy+F1BxxhQJWkkpBv95PFutyLb8HpccU5LqpjDat/Nj2SedWpHbe+43H+OBpY3BlXzxumb\nrIcnWUN9jAGjEH2EQLrf6hoeNGocdP2Y0txOl5i9lWsdtlDv/j64JGYWBTqgjhDiWnwP3FkJN/ge\n+3O+wxJ2iAL1hF8loHccdMwiHYRIXQlH0HWu2/lr34S6nLU5WG23TqadJaP47H/AdbjffBKK4Itc\ncbP/AGeptqCk7aS4Rza5F+O1784hyr9OTsTFVbsDpMUFREQ/eNom9j52IAPrsQ3692uHHVR4jwRs\n0tJWkd0kX7DjqNvnhgKQaPVqSlX6yN+uZA/c+8hSe25Avv8A0kSjo8InYK+sIgk6IVZEO4AImT/e\nD00IgA+3n14UvZBUpMaY1uthfvWG+yzsSdztfr6G2JoK/bIlFq9x50Ihl5R+8NC9B1DkWH+Nt8J2\nLbqqUfPNh/r4p2j8QQ2JigksBijsNCH3BEP0D5cGavLEjyoLttSkuNgHrrRb16jf+B2xC+4Ws+OM\nKN4tYpzjVr3SpakG3S179bHsDfbEojJxKdvUOo5EDEesHDMwj3ATCXqJvv53oA8d/wAw4p02OrLs\nVx5N0tl1Dhvce6LXNr7DqbfS4OKlcp+jJ2ZKS3cLZWiQlIJuE8ahvfbYkdhzjVLquK5ZLDGtxMVF\nymi8AhdgA/ERBMf0ENdtB764mgwmcwFx0BKih11IJF9tZcA9L3/HbsKtDeSjINDmSgC5THlwlqPI\nSl0qSd9he/pbffc4m9KWavsVyjVXp+O0TmmglHyAD1rJ73sQ317ANBvt+YauVV+M+im2OhTkRwHf\n9h1II5/3Sd+/XAnNMASfETLOYmSVJcapElCxwbaUrsvYbFKrH5cYEcgR2FTarfeFEGzdUBHYl0Bi\nF3vxrYD27+o6134fpkKMiFGmt6Q6mSzc2BN1Am/fnfYdul8N7GYm4/i4KOTYSHXBbrdbS1b/AF+l\n7Xwbcg2dpK0BmyIICsv9jgcA7j9xVv1/j38/x4zakImOZspi5KiWGZMgAqO1ltupBNztsR0PS2KO\nRsvml54qEwJA0pqu45OtqQEk8E3uN+w64HluYv4muFMcDlTMKTffcA6Th0AHftsQ9P7/AC+V9uE7\nVKQWNPmlxxwhNrktpCwTsDyOfS574q+ENdcqmeqsy+SpLSJbqbk3u04FXB9CNvTfnfBinLYwWxYs\nx+6C56+RsACH+sDUhREBAd77bHYeB88Zs+1PfzVSGnlKMcVplw3JOwkX43Fhfc3+uJcs5fKPElVR\nSLhuruSCtNr7yFnkcbm2/wDPYXoDIw1TFRMFCIos/iF0BgDpMUTgAD2Dv1b8a9R40PO9Pp7yYhSU\nF12a00RsSom4v1O1reva245oVcNY8UHIT4BSqa62Sf8AdUpIJuSf2ee3XsZsWScSOPWH1r4QOCpP\nBW6gADidR04P5EREdgbXjt+e+EHO9YqbQlU9pTnkuNNMpte2kMNpAuNtikbdehtgP4h5dXN8SZUt\ntBVpfjFpQFwA2wykHuLaSefhffAdprt5GISyzTrKk9kHzgBKAgXpFdUhdD4ENFAN/h6caDX6FHey\n0y64U+axTGQRtfaOhaud73JPrcj4nPEDMbSs302lPpCvZW4Eff8A+00tR+qibfHC39s5L/bqfqP+\nPGQfo+z+5+B/rjWPsWH+4P8Al/xwBFpNwR0oisRQEz9RTGFNQC6EdAYTaApQ799iGh79ta42dEdj\nywtC2ypG9gpBNxzYBRUbbcXvYD4fPqae+tnzww8ixBWVsOpCSLWUVKQLW6lRta3N9kTcFSOzt1fv\nJLdg34Hf7ohsB16b7jsdaDiR+UhUbW3stroLk2A3HTcevfnuQMdHlsygLLRYOc7gHc7cm/O3F+2C\nLWICSeEXIwiZSSBucpjDHRkjIigY3UJAW+pNlwSFUCHFP4gl+IJDCQDdBtKs+Q9MSHGUuuLQAFht\nCl7Hi+gG1rbcbdTY4pVOaxFfbdXIjspeb0K859pnWLXuA44nVYkBRAOkKsbXGJRJRVlBmu3CsWr4\nhEjHT/7sz/cofvEDUcPcPIfh8+0tLpsgyY8ksPWKglY8l0e9Yc3QLX436HnAJE+C1J/7dB8t4WNp\nsSwVa+4D3W/Y+npAWVdtbh6yUUqlrOXqBM4jV7B3T7gID1RoeAH8PGu2+HWcHIkdwstOp1i9ktuG\nx67JR8+Ob/DFiLLgqE6C7OgaDdxkmbEPuK3skl+3uq277YIitdssORZsFXtJmrtExQAKxPiAdRRE\nviOENgPuPtxnrUKRUn1KDD/mtOBxP6l0fdNzYlFt+bfh3tx6lEfisvmoQPPgOAm86ICUoIB/78XJ\nSBuL3O9+LDBrTbaqZRylVbUJmLg5g/7sWAPuCImKIbjQEdCGthv8PIC+Tis0xDK2XQ4EAD9U4T92\nx/Y6c9+pHGGCRWqe3V6fKTUIHkT4/s79p8O3vAaCQHvUp3684k1rgbPIKwj9OrWoTuEEkHABV7Bv\nqAvwzAb/AOzdgIb2Aj8/nwq5ZjPxZUpt1h4tlZUkll0CyiTcXQO5F7/HfBmjTIDEas05VRp9klx1\ni9QhW3uoWJkb3Pb14tbC+pwFoRh7HAOqtaS/EQFdEpqxPgAnADdiiMboR3oNeo9/wqZkhyU1GI+w\ny+pCXrHSy6dtQI3CD0J62555IxVShSzQqsJ8APRJHsrx9uiah5S9OojzxsUi574Yoqr29inCzxKv\na9sXpCH1WbABg+GuBRESjGgYNkMG/QQ3oeGSptqmUhbAYd8zQof6l251NEg7JF9xt/DF6rVinHNL\ntOM+nmPV6Y8i4nw9HmBrWi6vPKQbgixNwTf0wRnkFPWG7ImGsWjoeQq6fUNZn+n4iIgoXZhjunqA\nA9e+x7BsOAWVW5dJaUXWHwFSE7qZduQoEbjTfpbj48YBVd2LEyBWoTdQp/msSkuNpTPhlR1IVuAH\n9R3HQfgRiPpxNxgFbHCJ1m1AgdwZUALWp8SiVdApe3THCHfWu2/TfgeJ5NGNVlqkpjvEoUsWLLgv\npWpQsCjgXvt9OMXKJU6ZKyplWpy6hA86K0mMsrnQ9aVMuqKbgvhQuOL+lsS9tVJ5/iMTjV7N9Ybx\njlLoNWp4FPiNlziUen7NA47AA0IBsQ/LiKVUZKH26cWJBHtcZX+oeKSk266LHn/LbAWoCH/phpda\nbqMAtKehOFYnxNGh1pP7Xn2B943B+GBvKV65FiWInq9sFMpmRwKFYsA6DqIcA6Qjvw8h7dx4YJlJ\nEdEWY0y55hdN7NOE3KTvfSSDzv0Pww9UXNdKV4hVGk+309OpE0BZnRNBPlrt7/n6dweQdzccg4Me\nSWM1JVNi1Qq9nOqu6jDGKWszwmKAHJ1dgjh150I+waHhJojVSk5ngKlNSfJYMlAKmndNihQ5KLdB\n337jYAvDuHBo+Z6tNE+nItEqdiahCTqKmnCm59osfeAta5v+I2slauzKETSPV7X0HEqHSWsz4gBR\nIYNdIRw9tAAeO2gD305VimtJq9NdYZdKtSntmnDZSFNqvcJ23O1/XjF3wqzRBqmZqz7ROgIDLbjy\nFOTojYJS8DYFbyQTueN97WBwX55hKK42Wbp1ey/WRhUkwKFZnesFAQIXYB9nbEfw2Pr3HhAfFWlZ\nkp0d9qSWRVW1G7L2jT5xG50WGyhvfYWN8DsrxYTHiH9oe305KRU3XVOfaEIApLqzuov2Ox29NhgW\nR8TdomugROsWsqaaAn1+zNg2PXs2tfZ++4m7+4/gIA65uoLaww4lpxa3H0IIS04eEnsk2FgN/Q29\nClMzNTKx4gvRHZlOA9odR5qp0QI9wKT98v6eEgixt1GDNjuryK9HZKOaxYiuRQcmXA9bnCqdQrrn\n7lNHb8CGu3f2791HNlZqzSJNPajyi2pptlBRHfIt5LaQLhGw237W78p+fYsOV4iyJrc+CoNyYym1\nJnxFJshplIN0vkEXBF+O+wGBj+y85/7MWf8A+F7D/wDTuLf2ZM/2D3/lOf0xuv2tG/8AmNM//JwP\n/wCRhRbiCrW59PY/fYLl/D+sIP4en+e3CTRVBur05y33Jbaj67KG+3qcfRHiKr/3DzVckj7Ek3HP\n7TWASgkUxSCqOzpABRN66APumH5dtfmA6Dvxo7i3G3jouWnNxtdIBtcfHbp8txbHwZ7V7rrBNrkl\nIuPiefToOl/S1lsCYS5lM6OrJGct+O8m5BkK42jXlsb43XcNgikH53qUOvNLkmIZoQHyjKRTjiLr\nqqqmbOyt0/uq7u0igVaoPvJpkaXISlKVvCMVJCEuFYQXCHEJ3KVhFyeFEbDCBmrNmTcuMRjnKsUS\nktyXHmqeusJQvzlNBtT6IyVRpDh8oOsl4pSlAC29at04FmV0864nuz2iZQRy7jm6RIIBL1G5yV1r\ns7Hg7R+M1VWj5B+iodo+QEHDF83Fdg/bj8dm6XTATAzsQ5lODsSZ7Ww+1YqbfW8hwAi6FaVqvYi1\nlXKVbWJHFqjKy5mWlN1GhKoFWhLKlRp9OZp0qK8plRC0h1ppSQtCgUOtr0uNKGlxCFWGI/XrVcFf\njEPc7kByHBVIRt9mDXT3MUdy3YNb3sdBrfrwv1qoyACkPv8A3SCA87vtzcLvz8bYYXafTm2ostNN\npt7FDg+zoXCvdIN4/INt+b7ckYMUFA5xy1BZFfY9kbnYkMPY5mMuZBXb394wCv43r7uPYzFlOElZ\nGKkkiydyjBIWMQWQllvrHxGzFZNNVQkeWIlTlSnZLCpDzLEVyVKJlK0tMtKSlbhDjo1C7iRpQFLN\n7hJAJwKlT8rZcnU2PWGaZE/SqpMUGjpXSWnhLrUpt1xiECxCdDCnW2XFedILMdJRpW6lRSFB6n3S\n4kk3Ldzc7kZJ6kJSddvspih1lESiAjLCG+vt2HYefHm3mp99tpDjD7wsdwl90cDcbLHT42sbYItQ\nIT0F1g06nedTpKlIUKdBuWtepB/7PcgAWN7jbDFMXm7NV1Gn7Z3PpZvCCGrfZgECCfQbH7V3rfne\nwEPTtxJSvNkwTID7/meSSf1z17p/8dj1/HD2Y9IZTAnGmUry5iBHeH2ZAIClgAE/qAAdXXnn5SSe\nu9xaHipNvc7iCcgzKRQAt1k6Pih2NsPtXX7359xH0DgPEkvTJLsZ1+QVMuEbvPD3Rx+38DvfYDvi\nOgUamFNYhLplMu1JXIZ1U2CbBQJFiY/oLWJA/hIsdzORrtHvKZAzuQZ60S8wzjK7CxVjtb+Yl5iX\ndpMYuLi2aEmdy7fyD9ZBmzaolMdddYiZS7Nx+qj06NU4kVp2U4ZbjTLbTbr61uuLKUNtoSlepS1K\nWEpA3Kjta+BOYGaHGmUjMMmLRocGnpdcqEqRCp7EWNHhoUuU/JcUwG22WWErddW4QEoSpR9SPlrG\nvMrysZKp1Tzg/n6raZCMTllIJnmKLuriPZKyDyHcM589Iu1kZwE6zkWDtq/rsyuzmmR0utZkVJRJ\nU5/MVLqVMpTrb6nWJiW/NLaJoeWjSSNK1R5DoaWlSVJW2shYO5AFjgXSM15B8QmqqcptQqjSpLLz\nLE13LEikofkMMNykuQk1akQHpcR1l1txmdFQ5EeSqyHCsKSILM2e1ylulCN7lbwIpEJLlKS22QoC\ndI/QfRSyoBvoHY6AB7+fYLlKoyENo9pefPmPLRdbzpNlJ2HvL7335x+rFPhUzw5eLVMpweizlFKv\ns6Fr0my/vCPqtyeSB2xHmuSrswr8zBnuNw2m5fJ9RrZYzHKVQTCAAcZTqDz26TBryAaDiGXDkSKo\nZKJEnSlSFBKZD4SSgg7AOW5G/PrhppNNo82HlWuPU2l6nYUELvTYIC3GQEqJHkWJNt9QJv3PErmb\nLaV8cs5BO428FBYRphMW3WQDAdNQiag9QSvVvQDvYj6iPpxO5XHnXo8AvP6ky1AjzXAbEKsD73G/\nrtvfnC3TKBEZ8ZnZZp1OVFcdfT5Rp8ItWWwog+WWS3sCDe3PG/EJlb5eSpRpFLlcQIRw13/3ushR\nECnIfQiEoAjsCj58h78X5MZ6GuNKRIkXX5hB894gEpIsQVkbXv6/Q4eMrroUzNFepaaVSS41Em2H\n2ZT1WsCj3QY2xAVfYc2PU4JuSL3YXUHFoNLhbCqrv2gGFK2WIhukxDFENllAHQiIbDxvQjvtwsUS\nbUZmYGPaZEny22H0gKfdCehuQV2JATcXud+dsA/DvLMClVKvS3KXTiEU6cqzlPhOJ1JAcSQFsKCb\nEXukXAJ4scD2dvd7bRJED3G5FKcAQAf2tsYG/dENAb7U2OgL5377HfDDUmFM1eG41IfJCvNID71t\nnEHcBdjuQLHbfcEcFvDX7IrNYqi3KRSz7OC6L0yAof64DYGPYXvyPobYJk3c5wcenOlcLYDoYtvo\nxbbYgU+ICaQD94JQDAO97EBEfn34VpNXqsuvQojkiT5QqG4DzwBTrUAVaVgHYja3pgTlnLUJvxBX\nKNLpymzPfUpKqfBUjQpblhoMfRaxHAF+fhBYzJd6i4AE/wBsbj0ERMbrG2WMxh6tjrqGTERABMGh\n38g78Hcz0x3Wy6JL4LjqEgJkPpsQnbYLF+L7bfIYMRGKFWc7vxBSaXqDzidIp0DSS2kjYCOB+zuB\nbcXxFf6SLp/7ZXL/AOLrL/8AVOCHmvf7Z/8A893/AK8a7+jtI/8AlVI//E07/wDiYKttUBKuzyg6\n0RisI77f65A4x+io11anI396UgbfBXbGxeJhUPDzN5TfUKDJItzfzGMVoUlgTV6B2HUPTvt3Kbeh\nAfUQ338a0PGwogpU2Dzp3HWxFhv8T+HrbH8/VIccu6LggG9r9Cbnqbem9xa5GOtf0f8ARsiZc5Jv\npWce4vqFov1+nqTygJV2qU2OdS1kmDM89S0nIljI9mIOHH1WIYvn7voMBUmDVysqJUUziD1l+I6/\nQszMw2HX33GaToZZSVur8ucpaglA32SlSiLW0gk8HGFeKlSpdB8R/Ays1ufCpdLj1PPplz6i6iPD\nYCssR2WlPvOXQjW88203cXLi0JQCpQAsPkHAkJzGX/kc5Hs43adU5tsW8i2bIO1Pq/aYC0S8HmiL\ne2DKuA8C5In36NhbybyvUSHl4axREZJGm41zJRrJnLoqvfiL35kVufJo1FlvrFVZok9twtuNuLRN\nR5kuBAkrIcClIYQtDiEK8xClISlQKhhfouZpWS6b4k+KWWqVEHh9XfE/LT0FuZBlwY8rLb6IdDzV\nmqjRWlw1sty6nJZkQpL7IivoZfdcjKS1pQGOSblxwVGuPo7MrZyaX6xTHNBzWWOlROOIk1EVqLip\n44tFGqMRJ3KGtcG+dytZmMozbqCu7FJ71S1TZSEfBtUJcizsybSaXTFyMpzaqJT6q1XX47cNv2Yx\nzHhvRmG1yWn2lKcYXNdU1JQFWcYSpDYCwo4bfE3OWaVI8ZMtZYcpEOLkjIsWqv1iSKoKgioViDU6\nhJZpsiDKabjzo9EjIlUtwtWYnuMvSlqjkN4tDjWK5bXXNR9LzWai8yljXGTTky5t4nLEnYoyi2Z/\nASkZzAQje0r4jqtMTrUaNUbRTZBlQ63ZHSMkk8+rtZiQSjwEyTlRI9Mbqub2YyZcWKIVWTKVIEZZ\nQsVH9aYbcZLaExggJTGacIcTYJcUBYjN8w1DOKfD3wCnz0USr1xvxEyM/QmYTtUhpksOZTkOQkV+\nZUVzHjUHH1Kcqc2GgsLbKlx2lO803sXIvjbJK3IfZeT6z5HCj87Fpt2OYeMz2nVnV7xjeca3FlW7\n2vaHeOWTGvzVeZRbpe1tfsVA6os45wyI+WO7SKyVa7QWZk3LrVLffVFzHJkw225wbU9Dlw3kNSlL\nMdIQtkNLL6dA1BKFJCzqGnTaF4p1WhHxQR4gwaP9o+HdLg1mU7lUzkUyuUut0x2bSUQ0Vdx2XGmO\nSG00932lYT5r6XS0kNqLsAzfyv8ALfZcM5uzTypXjMllLyw5Vq2J83R2X4+ioNbbE3iRnK5TM1Yz\nUpiLNzBVeXudcfwbqlWkkpMx7F1HShpgFPiN3Vo0qm02kzJlIfnOsUyU3Em+3Jj2ebkKWy1Oi+Ql\nPlsuPIKSw6FuJSUqLl7gn6Jn3OjVXoGSs/0rLcBzONCm5jyo9l16qKepsmlsxKhUMs1wVJTiJc2P\nTZjclqqQPIjOvNSI4jKGlbdtMqfRzcpUNkfPnKPTMv8AMDI8yOKsEzPMZQpOyQWPE8S/ZcDjeAya\nrie0qRzVK1zNulK9JGkjXGKSrdbi05CPjkY9++ipEJORzKVDjVurQYsyqqqzVONUZU43FFO0Nxm5\nPsbuhIkOSFtK8zz0+U0gKSgJUpCipeyp42+Iy6LkzxKqeW8ns5HzFmmFkWssw5dZVmMvy6zLoIzH\nBDy1U6NAjzGQyKbJVNmySy+8p1lmSx7PVz6II2PUPpD+WxK7sri9CftMe9x4FXc15Bk3vqMa+lYd\n5dU5xs5Vd1RrHN5VRZtXjtZ8J0sK4buSsUHyao/LSYM/M+X5EpEhTjE1JjBgtBKZiG1ltUkOpUSw\nlIWSlkJd8zyiFABQLZ/aBTWz4O+JjNLdpjYp7Ly6sZ6Ji3FUZ91mNMZpJiLQluouSVxwlc0OQzEM\npK0F5TJTJP6EuU23QnNHzX255zOR/LlizMsbQ0KwzkMSO+YTKWeMgzVknbS2aW1SFHHMNUoFsxf2\nwz6Th31iexS7GKXWGTFy7NKItLJr0+WqqIozcuPCSyVw1VKZU5vnuPJQ95fsrbLbaFP61oU4pKkI\nV72pWKVQzH4hwq/4WZOp6ciO55q+WXqiJnkZjRkuh5TpsSFApypFO9r+235shS2oC2o0luG3IQ6+\n0lLIQ3goY1+jvx+/5uMo4wncyWSOxA15ID85mHcxuYCOQcyOLpxCnTkNJZBrKSD/AOKaDg5a0M7D\nF1pVgvITsAyWjnkaykDtUZhkuEh6Wyai9GgsUhVfhVEtJ2jBDLwXLYSleoNMrfDrbJQpbjSdCkJX\nYCs1+N1Vd8OKY+zleA5mWT4oDw0zPlduW84iPXYq6pBms0ScpbNkyZ0anuw356HkMRJjiH23nWUu\nq5jZijMWq5SyaTB7i9vMVJSMarS3WTG8MzvjqOXhWJXbmyNK6UIZq6cTJZJVs2YlIDeNOwRcFK8T\ncFADTZNNkSnBAMtcB0OCKuelpMxSEoRcvoZ/VpUXNZSlJGlGkEagcasqfmCheF2VVZhRTGq/Hcda\nqKKIuS5S21+2OpaRDcl/3lxtuMWErW5fW+HlNnyyi42CwKHpBYkxuyRDJCHt0LGMAeewgIa8b32A\nPZZXTSmruSgDpQ8FjqNtr88WHO3wxrMBllys0usEpC5ceK6D11LjtpJvfe5uPS+3GJHcWKYQMY8S\nAAMorGmKJfX4yIb+Xk2/T8vUl9pJlOxItwS2XgsdQUmwv9Lj+OEfI8SRE8TMxSnNRZdaqSR2Avq7\nD90+mwxGX0isd1EJrjshHzYwgIdtJqpiPy8b7b9fx46fg/Z76X2wEqXHeKSNt1IIBtfufp35DxlW\npx6i7meOyR5keJISo25LiXGr7bmxIt15ubbYmeRlGS0dGpNejrO8IA9IbECikcuu2vUwAH5jwGoj\n8ifW0+0EkIjuAatxfUk7X3FwD8bnAnw6groz1elFJSkQZCzcHdSFBy42sDtz0J+JMNk5NwnDkaHE\nwJmIVIAHetAUde4DoCh29B9eCU6ntsViM4mxUFB47C+y0km3S4PcduuxzIVQZq1TnyrALZcLtzva\n7tib+p9Lbb98TaXbMS0b46Yk+OZg2HfbYmECAbt5DuPy8jwJmVSTMq8WIu4QmYbptyAVAXN+LW+X\nUjgHlmEtnxBdlBJ0rmSb3BsEkuWPQb3v69BgR9/7Jf8AhN/hw7/Z6+6vqca/9qI/IH9cWNvRTGqN\noKX940W4Av4/ET4w+gKCK5SVq3Sma2Tfi2lY3+vONr8REheRM0pPBokgG/Fitnn074qUbqctwEQE\nF0R0I70YQDff0H/p59eNlL/kO8gtODbqAdie+1uT2+AGPheO02l91lVhquPkdrfW9yRxY9xjpbyl\n5JrFQ5FPpPK0+vcTU79fqbynsMfwqlmSgLZbnNczs7lrK2qLVN6zl5hWIgljPZtGJKsZnFrHWfFI\n0UMIn6ZNZiUfNLS5DbTkhmk+yNl0NuvFM9ReSynUFLLbfvOeWTZBuqw3OOZ4oUyoeKXgm6ilyJ9K\npFSz+7V5PsRlQae1NyoiPBcqCy05HjpkS0JaiqfKQ5ISEt3cAtWXljyhI4M5icH5niUVnT3HGWqH\ncjsW4Ki4l2rGzMft6JKVEQXcLT8M5lYo5CCZZ2eRMT+sVVHqWKdUHKdVoEpF1+yz40gJBPvpS8kr\nRtuS60VtkXuSuw3OHzOtIZzXkjM+V5C0oTU6DVaal1enSwtyE6YkglQKUpiyEx3wT7rYZ/ZSkW66\n84+S8ScvH0oHK5jOEmPq+EOR/IeJGEtIETOKMY8sWcX3MRld8qzRMsKa8CF+Yw8gigQVifssokok\nLlMyfDjWExIeb6PFYV/cMtSYQUoAnSp2orqs1RAvYtmUhCha48ni42+cMiUyu5r8EM7Zglsa8zeJ\nVLr7iGiQVOsRMsM5OobYWQm6JApTklpajpJnBQUGyDiNkfUTEPMZ9L+vP5swTYoTP3KBzQ2HDlio\nuWqhboO7K5ZzXEWamU6PfRz8UwyQ8iEHLp3j4hnFhaIIg7+rrMl0HJza/Z4UnNizLhOCbSam7FcZ\nktOIe9plJdZbSpKrF9SPeLNysAX+6b45DNUzBl7wBbjZdzPDcy9nrJETMEOqUKoQJFNcoGXXoNRn\nuNPNXNHS6tCW6sQiI6olGtLiVoDtgrmixZy/4i+h/tsra4STNhDmR5tbDlqswz9nMW2l0jIFvhYl\nCdlq0zXUlWhXVelpSdgU3DZI04jFLkixcKBrhcYrMRlvIU1TrbjlLrFcensNqS4/HYkutseatlJK\n06mVreaCgPMDZ0XIxczDkOuZnrP9oanR4EllOYcm5Bi0CbIZdjwKjUKTAlyFxY8xxCY7hblMMRZZ\nQtSYqn0F/Sk4C1+Rx9yd8qPOnjKNzlhTNVp5yMx4hYYraYXyHF5GUYYDxPerLlJTJd+LCpqo0OSs\nziXhKrF06wOW9qJKoSp1GIsWqzohOotMQMtV2AibDmO1RbAi+ySEyCYUZ1UkSHQi/kqXqQhLThDo\nWFbFIJwyQptR8QvErwvzA7ljM2W4ORsvVlFdczHSHqOheaq7SY1CFJpRkKBqrEJLMia7UoiFQVsL\nYCXA6pKMW0yDnHDjn6XvmWyY2yzjlXHNo5G75WYK9BdK9+x8xal+T2kVlrXYuxGfliX066sLB3AN\nYls6UfOZputFN26j8gtwtM1CnyM51aQiZFcjLo5jokokNqZW6aLFaU0h0K0Kc81LjehKiouJKLah\nbC9SstZla/syZPoisv1kVuleKtKqMqk/Zkz7RjQEeItWnuTX4Ya9oZiNxHWpbkhxtLLcZaX1rS0Q\nvHMT6M251Wm853JReb1Y4Cl1ipZPjDWe0WqYj69XoFiWm2NkZ5NzUq4aR8U0TduEG6jl+4QbpKqp\nkVUIJw2i5VdRT85w25LrbMduWh5TrykttNp8h1Opa1kIQBcbqIAJFydsbh4wwp1a8LvFKFR4Muqz\n63lZZgQKdGemzZj5qUB0tRYsdDj8h4oQ4oNsoWspSopTYHB3wLPVfN/Kzzf8m6eSsXY9yPJ81MVz\nO4ffZZvENjqg5BjkWNpoNyrieQp46dciZhhCu4y2QzeTcoknWJ1yRh1VUFuk3MDNSpEykszYMOW5\nWYlagKnSURI0sMIehy44lufqW3UsuJfaStQDoBSjfhOzEzUMueIfh/4iuUOv1qjUvJsjIeZGcu0q\nVWqxRluO0+t0md9jREqmyIz0lEmnSVsIUYj6Ul8JStN7gl5iMGp5ezrCweWKLJUbDH0Llx5KaLkY\n84hFVvL+TqTWK8R2nj91NiwXsJbLa383H01BsiZ3YmsQo+ikHDJZBU501enSTW6a3LYWxAyW9Q2Z\nOsIbmSEREJcMcuBJcDjqlIZABU6EakApIJy1/Jubva8kTahl+qxalnH+0bF8TqrQjGU/Oy7SKpWX\n3mRV2ovmohuQaWiO/UytWiGt8NSFJcQ4EcGKm/B3LzKS+xF3HNlAEw72dBQA770PYD6H5entkzqV\nUtuC8i4TdxB6W1p2622I25/DH2DnSE1UaAqnN2vGlqBSLEgKIUknY7XSd/6Yiq7IwR0qYmxIg/ep\n6D2KIqB49iiPYfmIe4sNPU1KQ8VAa1MBwE72KgPnudvie2Ia/WXaGxktAJGtMJhd77gFAFyOhAte\n5w7v54zyEh2hxHSJmIDodiPwTp/h6B/z1rhajQlMzXJNjYOOEdhqve/zufW9ucP8GCxGr8yUkAKl\nNSFJtyfNbKiB3BJG3pzhzuDAjYYtRLYGUeCAaAPAE6wHsHjYa3wUROFQfZZBBDccg36FRAI6/wAc\nIXhmxIg1bOEh8qLbsd1SdR4CXyob7jr2433xHnsio5exyS5jdAOm4mAf7IKlKO9h6AI7/vDzyYn2\nfKU6hICvZ3LHpfQoiwv6Cw49MPGV5seo02vmOblDLzJsL7uNO2G3Q2tf584k16TZpsGANxAFDuAK\nbQb+78M3cddg7+nngZS5L1Rqx87hDKrfHUk97G9vpfAvw+jqpRrLywoIEZbh1Ai5QsL69wDxcWO9\nsRx9LLfZANDHP8MUypAA+NlDsIB29C+dAIB6dhDi3KpyWKqy8Ei4WHNuh1Dtx+O9r9MHsoyo9RqU\nyUj77ThWTYbalkdODzuPTjGnRPcf8/lwf+0D2H4/9OC+gdz+H9MHe6v2Q1axAR6yOc0cv0pkdtjq\nGETk0UqZVROYw+hSgIjodcYpRI7xq9O1MPpSJSNSiy6lKRY7lRSEgDuSBj6B8RKjBVkTNaGZ8Fx1\nVEkBtDc2K4ta9bJCUIQ8VrJsdkgn06YqoCxCqdXgf3TB6CAiGvPbXfz899vXXvKK2tKtyN0ne424\n23BuBtj4UedcDiXkXBSTf5XBHqTbnr3xc/la5TWfMPTc+5Ps+cKJgTGXLlDY8l8g3C7VK+XUoEyb\nZ5CoVZKLgMex0lOLiadZpM3ihG6x0gkGqoIGbpvF25Wm0IVSLOkPzmIEemoYceffZkP7SXSygJbj\nJU4buJsdid0mxAJGd548Rncp1TKtMg5cqeZ6zm2RVo9Mp9OnUynX+xobU+YXpVVdZjIAjOKcRqWA\nrylgqCy2lRMPV5b6OLPOLMpWWt4b5pK7ZcZrZj5ZrzDWGwPcPWuRdnM0o+UisDMYuakH2MrWyM4m\n8Z2pixOWZSZg4dtzkjJdG0iAvLlQhzXWYVWQqMZdNkJccMN1SzaPL0FKFqVEeSCuM6lPv6RcEJWA\nLtYZ8XcuVmjwpmYskyWKunLmdKbIiRWq/BbbAXUaIXg49HaarcBzRGrMJx0GOp3QhYLzCqB3i+Wj\nIFps16uU2+sVwt9kmrXa7BJKApITVhsMk4l5mWfKAAFBw9kXa7g5SgRNEDlRRKRFNMhaw1LedlPL\nU69IWt591R95x5aipxajblSiSeg4AAtjTKXTIlNjRqJBjNxaZEhMRKdEZFmY0OKwiMzGZBJOltpC\nACbqVupRKiVE78pfLebmbu+SKaS2J0o9DwHmTO/180B9vDJmxJXELCNbK1LKw/1M9iM4KzGaFdyM\nWXqcjGyI6bmsRYZqL0hhL3kJYps+cpRb8zWIbPm+VYLbKS5e3mXJRYHSrYYB5yzV+hVFo1Qep5qT\nk7N2XMqhHtXshYFemrioneYWJBcERKCv2bQgPkBHnM7rwE3Lv4sOgsX7inwkjdOw6gExCG6OrsIi\nQTdOtB3DsBREA4TYLZ9rCre6pVz8+l+Odu47g4eW9LcxSVEFD6XG732JSCNunvAXF/x5wxQ3+lLS\nbVQpQMYply9gDawAB+oda2cQ2BhHZu298MdWX7K1GeQRocuhdrgb7K52BAtufhgEw4pb6ozit4T4\nS2om/wCpUvU0U9kg7bbfja0HOdy8q8pnMxbuXh9bkL6tQUqWClsSgzVtKULcqFV7wUCwp5SaMzCP\nJZiRhzjJOQcHafXABD6wDdOSoURVCm1CK28HzG8h0upQWgrzWGpBPllSynR5uk+8blN9gQBz4dZ7\nRnrJVMzUKcaS3mJNUQinrle2ll2l1afSlAyQxGDntHsRfCQw3oDnl+9p1qm2F+TZ9lS+8n2Nlsw4\nzjmvOLcLBCR6dUkiXq94dTrc8+gnC+UaADivGiJGYMyNJ1mKGfTLLRZjrnftFG6qXHUahiqVOhui\nZFSK0HGiWVefIieStTajJj3b0KWRrbR5g1pvdSbYoS/EhGVcteIlZTluuPueGMCNIcM9k0mlZkTP\njty226HWC3N89qKHfInP+xqMd8JSGXQtKgLbhhB3AYztGYAyHjFWOq+Z3OCHVAXsqbXLUy9YMJmS\nHIDGiGbrCfHqacMLJ9NGkzGZS64MyoLpt1XADzDDsB5xciKr2CruU/2dToExQCVq9oTHIJMfaxc1\nEhZKbHSSWjL2ZESc2igijVsOVfKrObW6siEpzL8ZKnIzIpTtVCkAVdXtIcZjeQPOjtlwlClpRiGW\n6jXfHsfI0rJVOsdHt0Y3h51at2yLcQ061i7LFsrFXnzqLekTeM0peEfM5VkV0kiuoxdt1jpJAoXg\nfOZkUysmO824yZDLThbcSUqs42FJulW4CklKhcAkEEjfF6n1OlZlqtKr1Gnw6nDRKlQxOgPokRlS\nILzsOY02+2S04WJDK2HC2VIDiFpCzY2hBF1YaWZOiCYCu2Jw330PWUhwDetdtD6D7cW5rSJ9IZPK\nmZKUk7dNQsbi/bc9e+PYsky82Vmlu/6pUduQhKjtqbUQe56K44xIYRQj6JsCRwKJwenW0OvC7Y2+\nwiPYRDx76HiiHlU+Q2m5CXIyUj/wrHH16c/XEGeKeKgmgFrf2SQz903KfKc4PrY7c8DpiHOUzpRT\nJbRuk3wxD2DpV6B9/Al7/wDLuYZbbeiSVCxWgk9zcjV1Hbve19+tjVQryoeeKBTrkJlNtIX6ktlB\n6fw9TiVPpcZN1BoqGESldogO/XqDoERD8/Xx34X4kdURa5G4GlfpsLmwNrWHTfexOGOHDZhor4bN\nnHYUoWAF90kgn5jr6dcJrI1I1fx/wxEBN8Q4iH/hnIYNh+G9DvtwSRI+0ZCgNwltKRuOqSk/E3Nv\nh3wqeG6HabR8yOyCTdSXAVXtazgO5/4t/wCJ4De+kDO12KKpjdP1lHXV3AAE4EMPb5DxCzG9gmuu\nAAENKI730Ejk9Tbm/T4YccuyWJtGqkhk31NSGSRbc+USO+4+HXi2Hi2tEGzVl9XN95RTQgAh3AEx\nHfbx+Ad/76sSW5UKgQsXCG7D098HsL7C/S3XffAvITaoH2w6vVp8ouEm4tpVcgfzI9fhhi6ze/8A\nAP8ADhg9jV+7/D+mCP6Rw/3v/Un+mB07D4hQXSKQFCmHYgUoCGhH1DQgICHfXkN9/QIozikLWy4T\npJPUmwsRuD32PG3pxhKS20tojQhKkDYhCRvbodItf03Fr7HGw7gyzYipdAcoFKcPXXb/AD57b0Ac\nep/VPltVyhRJBJ2tvt/LtsN8cssoeStpQ94Da/cDbjfcDg79sdkfo6qxAZB5HPpXKtaMnUzDUFKU\nbk9LJZKyE2s7yn1grDPkvIoKTLWmxE/Zlwk3LRGFYJxcS7UGRkGn1j6u0+sOUXLL7KF0rNLDshmK\n0pmkkyXw6WWwZyz7/lJccOpQCE6Un3lC5Cdx84eLL8qmeJXgc/CodRzFLZqniElqi0hcJuozi7lW\nO2RHcqMiJCT5KVqkvF99seSy5o1OaUKsZy6WLlY5iub/AJJOT2PRPnzlo5YuVPmmos3e7XS/sBTK\n11stMvWVrtf6ZUbQgtK1aMr8+3Yji1xPop2CMesgmhSbqps3SxCnO0udVaRRgDOp9NplSZU86yGz\nKdcaflPPNMuDU2ltYT7KVjWkp12SQklRzZSs65T8OvErxAfUMsZzzfnnI9Qj0qFUfahQqdEqVLoV\nNplRnw1hia/KjOO/bSYqjFeQ57OCtJcQmuNCuuKJvCHNb9IEy5U+XWHkse2blu5ZOWrB8hSVLjg+\nkO7W0lpOZybkCkzsiKeVMkEx/Gsmj6dtCxWU3cH8jZ3DArwyRE6DMuKqDVK6mmwEGO5T6bToamC7\nDZU8FKVIfaWq0qR5CUgrcNluqU4pINsOtTpFcj5kyB4WuZ3zbIRVIWcs65yzKzUhTszVBqnux4zF\nFpNSishVCo5qjrq2o0JJdjwG2YSHSjUVXpwLQcQUHm6gc50vGUHXcYczv0OGYuZi0YQrTqVgqlX5\n6Yph4fKdEqDkHjiVrtSnJatO3MGi0dmNX284uhFC3btGSCFuI1DYrKZjUZCYlUyZPqrkBBU2yhTj\nBblx2jdS22XFtEtgE+WHCEAAADOs1VbMFVyFLytUq1KmVrJf9ojLuS4WZprceVPmRYtTEihVWoo8\ntDEyoRo05tEpTjYEtcVCn9a3HVrotmpnTeY3kdwJzW0flww7jvMFW5uk+U+044wTQJKt0jMENM0G\nMyZilm4oUfKP3spYiHSUob9yzkFbJaGki5M7kjvXbIY8S0zHqlGp1WRTIEKa1VTS3o9OjqZjy21x\n0SYl2EqWVOAfqFq1lx1JJUsqUnS90t+q5Q8Qc3ZGnZuzHWaG7kYZ+p1WzPVWptUoEuJVnqLXlNVV\n1hlDMN1taao0240mHCdaQG2Q2275xn5q8Huw5GbjlrNGDeTzBnMhhPmUxtj41c5Tj4/hZmvY3ybX\nporzGee6Vjiy2mNhLjW5xmk/gD2qWe3QjJoshJr/ABjSRnlrM0FT2XJa5kOkxJ8CpxWkN0xTCVNs\nSW1HyJrDDjgbeQtOpHmqLuge8d1krvh1mFlXinTKTl7MWfsx5VzPk6sVJyXnkVSQzKq1GlRy3Vst\nVKqxITsqDJYWWpIhMt0/zXAWU6SyG7q8zq2IuY76Srmi5HLfy6YbVcXrl/Na4HmBJX3g5+hc7UHl\nYq2SadammQHUk6GMosbCQ7eoDjuKjo+FeIM1pSTVfOZyUQOyzFRZ2YarQnoEQe1U8KE3Qr232tql\nsvNuecVGzKW0hsMISlJ0laiVLUMImVm67lPwPyJ4nQM45j/9i5uchv5SMxsZUXlmpZ4n0udD+yW2\nEedVJEqQuoKq8h56SkvJjsJabisLFVeV2jUWFyH/ANnsyLXKbWoC5ZbtGcpfJNliIhkym7rI1rKs\ntDV5zaJRBIjucXr8MY8PELSCq6rGN/0RA5ENJguUGKzEX4fuIZbbfkPVT2lxKEpcfU1UHmmlOqAu\nstt2QgqvZGwIG2NQzZWapNy1/bBpEyozZdNodLyg3RIMiQ45FpbM6gx5U1EBhSi3FTLkaZEhLSUh\n10eYsFdzisbiKpFZ+j+yvzDGxnjK2ZToH0sSlTjpq/0mJuDaSpKeP7raHePLK0fAitOY8mJpJGQn\nKgs8Ri5ZwQFHJPiAVQoyRFYg0mr1JMSK9LbzagNuSI6HQuOYDr5jOBVi5GU6nWtkqCFK3IBGztQK\nhU6t4rZdyma5XadQ6v8A2e3ZUqNR6rIprrFVRXKdTG6zBdZKkxKzGiFTMSopaW/HSSlv3SQelvMb\ndcfZk+mHLyo5hxLgAKVlPENbxhD3dHEcA1yGlkLMXKjV18dTs9dDKupGXVpN5YQ8RjswN27mmspP\n6rFqqiBOpnrAiVDN8GFNh05TUmEqGHzDa9pRKmUtlcVxT5JWSw+EJjbAshatBucYh4fwq3lz+z7V\nM95czDm0VTLGZF5icpZzDLXSHaLl7PcxNcix6aA2yyKnS3ZMise8tFSXGCpCUgXHH7P9BrGLuRnk\nrhJGqV9vnPKeQ+YLJ19s60KzJdWVEo9oTwZSqgvOGTCTJXXllrV0sScKJysjSLUsgUgrGMYEh9lq\nl5fp0R1tAnzZdWqDyygB5MaNKTAjNFZGoNrW0+4lBIAUNXXH0blCpSsweN/iJV4syQvLNCouWKFT\nmEvrMB6oVanHNFQmIjgloyWoc+nRVPgFwNL8o2G2KCsHysa8mGY72oRI4l0IB4UKI+n5eO3YQ3wI\nq0RL4pj6RsptQ27jTt8740nL8tNWcq7T9yabUFab8hJJuBcW5Av8PW+HE4kcVNE+9GRBwUe4AICR\nz8QN+O4B59gDt68QR3yy7Jjq5WU254Lex5+O/Hztjmt09UrPFAqDf3Y6myVDtZJF/wARe23ww1Oh\nO0cxxxHsCiShRD0AClUD5eQHzr18gOuLrrSF04LTa5JSepOxSevTi23bnBamVoyc7VikKX+r9gke\n76lII6b7bW33th3cPftOXYFUOPT/AFhR/wDOQ35eQ/u8cC4jZha3Lfsgi/YKA468m99+MGTHbZoF\neZjkalRlggWJ1bgHtyeN9+LG4wjmkCtHrUqZvBPiDrXYSqAIe/kA/wA+lpl0zpDyrbWCRYXH3SB8\nbd7YG5KLlKytUlSFcPFRJFtlIKTvbi5/jjx0+O+VYpKKDr45ADYB2KOiiPj5/hrfFZlj2KU8sJsU\ntqJsP929uLDfsdj8MMFFcakUWoyGbHzGJKL8G/lmx2/gNxzuOJh9kIf7T+X+HE32yf3R9R/XGV+y\nvfvK/D+mAE3cCoQ5f9YBMAgO9B94fT376Hxr57Hi7IQG3Ao3sd734O19wfodhzxtg61zp4Va+/Cg\nehvb4EdLXxtbLFAx09jsQENfMP7vn/L16eQVNpUOljq55/D13OI1XZfB4J9DYg9bfO3XF08B8x1M\nxVyp892BZyKszy080Vb5foaiyUS2jFYCFc4nyw4vdgVtTh3KM5Boi+ilStYcYmOljrSACk8TZt/9\nIEvDqLbFHrUJSXVPVFuAhlaAkoQYkv2hwukqCgFIuE6UrOoWUADfGeZrytOq/iF4XZsjSITdPyXN\nzVJqbL63kypCa9QhSoqYKG2HGlqbfClyPPeYCWxdtTi/cxnyA8xFM5VeZqvZov8AF2ebrMNQczVh\nePqLSNfTqkhkTFlppEKsghLy0KxFm1lptovKKnkCLoRxHCzVu9cETaK80SpM0ypMz5CHFtojzGlJ\nZSgrKpEV1hFgpSE6Q4tJUSu4SCQFbDHXizlWfnfKcvLlJkQYsqfVcuTku1Bx5qIluj12BU5KVLjs\nSnQ45HiuJYSGVJU8pKXFNIKnEvfKlnvEdQwtnXla5jGOQy4czqfFttbXvEcfXJ7IWK8tYfcu1K3a\nomq2+Xr9etUDYIqRe1yzxLuWYPiMwaPGBzqgsVPim1CI3Cn0yopk+xzzFdEiGlpyRFlxCS06hp5T\nbbzbiVFt1BWkhNine+IM9ZXrs/NOW85ZPepH6Q5ZTXYRpWYHZkWkV3L+ZG20zoD86nxpcuBLiSGW\npsGQ3HdbLvmNvAJKSbi1T6SLCsDzOL3qQxZkV5y5Y55EbJyOYTxkEvXEb5KU5SuNYRlKZBsbZdGF\ngpW5v3lqnrRI11Ge/ZxaRi2UaznQZLuVCrFfhir+0qiSVU6PQHaFBi62xIUwW0oSuS6CENrfUp1b\nqmw55ZUhKQuxJzWpeE2YX8iewNVykIzfUfFOL4m5mrPs8tVMYqKJi5DrVKiLSqTJYprLcGLDZmKi\n+1pZfdecjealsQOP58sC8vAcmuOuVup5huuH+XTmjU5uckyOeE6JWr5lXIziKZ0uLrkdF0h1YK5X\nouh45RcRUHNrvXSkrbVUp40exaNx+tXI9Ug01mmMUxqW7FptQNVfM3yWn5TxSGQgJZK220sRwUoW\nVErd/WaUjmWZ4d5ozXLz1Vs6zMvU6tZ5ySch0hOVjVJtLolMQ8aiuU6/Um4suU9VKsUvyYyG0hiC\nkxQ844u6UuW+ZTk/Lyy8z+BcAsOY6Vms8czND5jTXXM0RjuJTaIxcrbJCXoy0dULVNuRPWkJ1P7P\ntzlw/eXyWk5Rw/j6u0i2KksLrFXpBgz4cBFQW7U6lEqBflIYSkJZL2uOpLbqlDy0uXQ6dRfUpWoN\npSnWSylkjPzGdMmZmzU9lJiJlPKNWyoKfQH6u+XDLZgpjVND0+FHbKZbkZYegpSy3TGGWUtOTXHn\nQwf8sfSOcoU/zD545xsT0XmHjeaDIuIJrBmOYK5J48QxFCIzeN4nFLjO8vJQ088trC7s6KzcRCeN\nWjaYr6ksinNlsgpSrtKMPTq9TNU7MESNOFQXHVCYQ75AjoDsZEX21wpUpwOIZSUhga0a7K12UrSk\nUrwoz3TaHlbwtzDV8qvZNiVqNmmqSKd9qLrElUWrSK2Msxm5MZqG5T3ak4iQqrLMeV7OpTHsmplB\neAuJee7EmO330RhZeuZCWbcgc5ltTLQx8ZX3K9jZ37JMhbIUMfFc2VmSVWZRDpFCSLYlKuUH5FEm\n6i7fpdGGw6zESrLLpakFNBEt6UEIbJdTIkmQPZgp1IUQlVleYWhq4JTvjQK54X5gkU7x6Dc6jp/0\ntRsuRKCXn5iBDdpFGZp732xohOGMhyQ0pTBiCcS0QVhC7tgFW3mbpD7kmzVyxt4i1pXe+89Z+aKF\nmVmUUNWaUVXHthqoxEi6JMGlC2oslLtnP1FvEuIo7MixwmSrFIipQVU486iu04Nu+fLq32iFkJLS\nWhGej6FnWV+ddwGyUFNgff4BcqBkWq03xFo+fFyICqTRfC53JciKlx8T11NytQqkZDDZjhgwPJju\nI8xchD4dUi0YpKlCwvMDnauc3POFyr575VobMSXNfcJLAsbZMdT8HVy0+JyfiOPocHTH2MrPXpt9\nOzUPKOawvKWVeyw8IjX4VkaSMYiZ5Fuw7l1VqsVanSqY1OTVhKgNPxXW2vKRLiIYZbVEdaWtxxpY\nY8xwuob8tIKiACoJW8jZTleHvh34i5dz1Jy4rIMan5qehVmJKmmoSaHmFyrS57VbhS4zUSNJYROT\nHhJhSJSpcpwMJBPkLdtTzIWzlw5mvpM+YGUu0SykuT3knw7lRSSr9es8hXoyxK4mbTCp4CuWKCet\nZIw5G5r8ovY+LNDPE155E+kFCM1zmTv1lqFUc41J2W35lHpFIkksIdW0h1MZDqg2262pK7yqrLIH\nlqBXfY2JOELw9j5tyf4E5VFDlOM+I3iRm2jwmJsuCxNeh/bjsZK5kyJLacY00bIVBS88ZLakRFJu\noFxKQeCUsgdWdUWBNNA7tmZU6CJjGRQU38QyCJjmOcyKInFJEyhzqGTIUyhzGExhTmJKXoUBKwAU\nOaSATYahx1JAtbfsNzfH0hR2V0x3NchKlKbcT5ra1AJUvQ0lQcUAAkLXpKlAAAKUQABYBrayBwiX\nLQBDRV3AD662bx7+2vy1vzxxOiaKkoi9lNtKG3Pu8jfe/e/PY2OGTLcpFSgU6quEFaXFtFR3+45t\n96xBttf0w+yoFXQiVCgBhODMO2h8o9I99CH73+djxCy+THUwoH3FuE89F3AJ72+PUcYpUynKZzxV\nKoE2SuG6gW2v7v8ASx9Nx1BwzidRrKJG0ICkImAe3fRhKI77eRHew3/Pi5OaSWGNI3cQQfXUAb3F\ntgQP8r4lyfVlVReZ4zvvNsq0JvewAcUk7E9gDt8xscLxXGRkkSH77IoUR2HgA3r19vPnvvihG/uR\ncWdtgqxt3A7evJIOD8xlKsrVJqOACuwGn94LAPHPO5/hfZPJpgzdt+jwUpVN7DsAG7dh+Qb9P13x\n2yv256QrbckbDY3Tb6777kenAxDllRpuV3w+QLOLClKN7haQPS++w4vY79cPf28r/kv/AD45+yB2\n/FOAXt0Hun/0f0wFEVehZT00Y3b37m7615Ae/r5H178FHgVNgbnqD2P4339L/QjHqinUlY2ULE2v\nxYfL5Y3LG6FSKlAA35/6a9vPv47ccsHW2ptW5Atvz1+d/X0PY37loC0BQACgOe/G/G3T15x0J5Us\nHYNkcF8xfN5zGxGQ77jXAFhxDj2Ew/i+1MqDOZCyLmKTfIRalpyC5iZ5zSqHX4yOUWfvImJWmJiV\neto5gqUzZRo+M0eFEVCqVRqCH340FyLGREjupYXIflqUE+a+UrLTCEpJJQkrUtQSk7EHIPEDMWYh\nmHJ2Q8nO0umVrNMPMFXk1+tQnapGpNIy6w0uQmFSUPxk1GqS3ngG2330x47LS3XUnWHG8MYcq0lz\nwZgy2PJxie949xXQsX2HKDmDuspaszPa8rUaeSWc0BO9VanNgnbpkWfZyjTFdfk2URIy7RNZI6rp\neIegf2LSzWZUxNKivR4rEdcgoeU7LLZaaK/I89tka3X1hQjIWEqWm+6ilV62Yc6t+HGWcurz9X6X\nVK7Ua1Fo7UmnMwsvolCbUFMJqZpk6oLManUmK4yuuS2XH2Y7ikEJbRJbtXet8uvMdbZe5Vyr8ved\nrFY8eCJMh16CxBkWYnMfuAbA8Oyu8VH1pd/VH6bcfjiwnW7B8ZHaxGxk/vcD26XOeLzTcGYtyOf1\n7aIshS2DYqs8hLeppVrnSvSbWsLYaalnPK0Bij1OXmrLcWJVdqbKk16lMMVRtS/LDlNedmJbmtBY\n0+bFU60FEpKwdsE/l85LOYHmeomdMi4tpNnm4PAtOGxyqMZRr5Y5K8WIZiMiEsYUFCs12TQl8ikT\nlUZuSrizpvIxdfJ9pKslyLIpjfp1Elzo8yTFZcWmE0VqCWXXFPLK0p9nYDbagt8agsouClHvEG+4\nHNXiHlnJtcoFGrtRhR1ZulpjsrfqVMhsUyOYz7q6zVFzJTKo9JUWVMNS0oWy9KPlJdRpUoQa5Y6p\ntewPjmdTqPMBD5qkct5XpmQHdwpgRGFHDCoqxjOCq+OpdWNbzMjlCAklXTTJNaeOXLyEdLEaOY2N\nULH/AF79JbYZixVhuaiU8/KYkea0ERClsAIaYVpCjJbVcSGySpCiAUpOnUQok6pT69WIDk/K0mgU\n6jUOpUZMCol/MiHJvnOvTqqwHlRmqJLjhCqRMbQlElCCtDzoLvlFvE3I3zQZSzpirAB8NZMxxdMs\ngycxbrJmL8k1iKiKcusi2e5HnSK1RSUQoUOs5aISdjQYqR7V8/jI5y6au5FqBhcOg1WZUY1OVElR\n3n1621So0lpCWCoBUlV2tXsyCRqcSCkLUlJIKhj2veJmRqLlav5rGYqLVqdQ2nG3m6NW6NNfkVJK\nFLao8XTPDC6q+EOLZhqdS8400+8hC0Mrsxp8vKGNUOZ6Ez3jTmbr+TsTUyOmMXDA4xlIanMXq+SD\n1b9uc3Et0IhMVvEFphWbotJsrUzFpLzLgG7SVeu0mrF2ZXBMeNWIU1iel5uKlyNojqS2k+cWw9KL\nqApuO4AQ05cBSiUhRIAIGXmwZikeH9Xy1VcpSabUKo5FrIkVhl+e6gUtMo06gCFIUzNrUN1aVVCI\nQ44wwnWplDZW42EGuHctXCoXfJVOxZkqz45oenV1v9fodqmqTTiJEIsqa02yNiXNfgQRSUTVdDJy\nDb6qkomo5+EkomcwuixpTjZeTFkOxkIU2++2y6tlroPMdSgob5F9Sha4JIGNCzHmOgw4ceizK9RY\nVcnaXaVSZVVgxqpUVIVt7BT3n0TJWoBSUeQ0vWpJCNRCgFtixFlqEplWyjY8WZLr2Nrw3K2qWRJ6\ng22Holpd/BUWIhXbhJRDavTSyqKC66BI6QcGcoILrtgWRRVOSm3EmQUIfeiSWovtSkMSHGHkMOgk\n28p1aA05sD9xZBAJAIGC1HzNl6qInUOHXqJMrcaJ5k+jxatT5FWgIWkJK5lOZkLmxkBa0oUp5lAQ\npaEr0qWAVGG83ZPwjZUrdie7TVBtb2rWmgurFX1GzeYJWbkyCNsLBi+XbuFoty+aJplQl4wWc1Fq\nkI6iJBi6IRwXwvS6bMnyYD7kZ1xpxPmt6QsNSEgOhKiDoUUba0WWnYoUki+IZWXqFmvLbEDMlMi1\neDHnQqgmHMStcf7QpD6nIbzrSVoS+lpZJVHfDsZ9JU3IZebJTgWu0wSWlCgURKRcFyh+9oRHrA33\nhHZijsQOYRMBhEd9QiIzNKTIdhk8rjpbVcm5KRpGx55Fuv44tQ3DTKPU1EkBuW46m2w0OL94DoB6\nCw4HAFpK1fEdyDA4j++zOmIh6mMiHYR/EB18x7b1wF8tUdtaT/3UpJ9BZwjbi43Hp8dzgoGG3KVI\ncFv75GQoHuHGyNrc21W7jYYYfgCklKjvsksc34AYm+wdg+etcMRKZM9jg+Ywixv1TcbfC/5BthKp\n8t2h5MbKiUqROI3vslayk+n7NucLE3hjoRmzj0kM3MACPoAl9t+P7/IjrgKpjQuUAAClbv8AE/j8\nPnbpp0JbS/Z5AI1zISFAki5LjQ426b7n5eq2QKVSQIBBD7wLD6eddQa/T5ee/Yd8Ttvl1LCV76Cg\nb9rAb+p26dNiOAs0OnGkRcyyk3Cnw87bjZJUvp8uPlhtQVOg7+J1AAl+9vfgOkQ2Gvw9Py4knNJU\n4UIBspAFun7JI45P9cXsozlzssynZCgQZbiPe7WQR14vt/jhSooZ+7KUTb2mbQ+fHfXntsAH1Hf6\n8V4ZENTilCxB/Djgfnbc7YKVBjzMtPtsqt5hQQR3C7E7X9b7bG3e+Hf7K/3y/r/z4ufabf7v/wDV\n/TGX/ZUr98/85/pgNKGEFjGL/a2ID+Pf9S+e/n+EqSCjSeo2Pba/4HjnDo4m9+Ljn+R+RHXn5YVq\nG2kBv1+fvr08h/P1DXFdrZ1Sb8nY/M7/ACxNbzGbi1wncdTbY+g79Phi2/KLzgWvlSnLrum1XMGF\n8rVpKnZ/wDkJsD2i5aorNyo/RauTdCitet1eXUdSFJujIhndek11RWQdsHDhvwXp1UdpL7x8pqVE\nlthmdBkJuxKZSdQB2PlutklTLyQS2onZSSQc2zrkGBnyLAQqoT8vZjoM1VRypmukuFuqUCqOIDal\noF0pl0+YlKGqnTXVBEthKQhTbyELx2ZwdimD5WOdjmgrXL9ccgxOD8u/RPZq5psXQMhZ5dnYazBZ\nGw4xs1Lh7WaPlAB/a8cvjzTKt2R+dxYGUa6bOCSQyDh+/etkSIim1mppgvPJhzMsTKiw2pxYW2h+\nIHWUuFKrKcYOtLbhu4lKgQrUVKPzxmGvSM7+HWSns2U+lSMy0Hx3y1kqsymoTC4kuRSswOwanIgh\n5kFmDV2kx3JkNtKIzjyFpLIaS001Rrk6jLXS8e1DnLzVzb8yWKKHauaem1CjVXDL6eu2Us85xpjG\nBlZ+z239qsg1WntarVIKRaVueuF4c2mbl28lIVyJiVUwAj0RSkusMt1eZVKhFYdqTLTLUQrekTZj\nIQpxx3zH22g022UtuOvF1awpSEpI+9p2fVwanUqr4b5byDk6u1WnZKqlSqVQzEiLTKLlbLM56SzF\nhU4wqVOqLk+dLZXMiU+mogxWFNNS330kktX0vtls2O86/wDaLIigWi10uNgaC5uMFH1O0T9bZwlu\nnMq0dzL2aFawkixRibE/UfOU15uOTbyqzVX6mo7M0KRADjrrjE7PaGXHWkoYLqEturbSh1yS1qcQ\nEKTpcVcgrTZVjpBttjLqdBg1fKf9keTU4MKoyJNWTTZTs6FFlOSafFolSSxCkOSGXFPxGktIUiO8\nVMpWPNCAslWK80PNzTBXJt9FVzAWqvuMjNccfSIc1WR7DAP3pV5K0DHL1t5JKBIypliK2MVV1pqM\nkJVRQp7I1ZOpBcAOu4KITNEKj5ZqDrZkeyZhqUlxtSrqdCFoK7KWSC5ZRWhayf1iUlRtc4dKllk5\nn8RfHLKcCWijqrfhFkikRJbTRSzBL7cxDILLASUw9KExn2WACIbjiGkkhKCcMUVS51f6SL6OrPdA\n5ocq8wPLbzTZ1uUjie53S3XdneoIgWWQeZjwZlGsyk24Ti5yuWhxCHsEewAKjcyMYuwJxSJ2bfpt\nQoz7eZaFUGKnKqFNqkp9yI8+8+H27OFcuDJaWshC23CguJTZp7SlzTdIwp5jqlNl+DvitleqZIoW\nVM45Jy5TYdfp1Np9NcpckqhttZczRRJrEZBejTIbclMV129QppdfiF9QcVeqmGLbbLXiT6cyVtlm\nsttlWmBmLNhI2qwTNlkEY2J5qpUsTFIPp16/dpRTAAFKOjUlisGSSiiTRBEhzlNz563Kbmp9bi3H\nEQA2VOLUtVkVU6RdZUdKUkhIvYbpAGDNRpkOBnX+z5Biw4sOFJzOmX5UOMxFaLkrIzQkvFuO22gu\nrUAp1zTrcUkFxRIBCP6S3IV9xbO8vHKxjq2Wqp8u9X5H+X99E0SuWKwQdEyS+y7VXN0yXebpBRUg\n0j7m8v8AZl3TeedTiMkVVGPUatiIAK5D18wuPw2oMOI46zAiU2nKDDTjiGZHtjZekPPIQoB5Uh0q\n8wuagbWFt7k/CWHS6wvM+aq3AgT801zxEzfFeqk2FDlVOjpy9NTTKPS6dKfaW9Tm6XBS0uM3FUyQ\np4LWV+4RI+fmzn5t8bO+e7C+W705xA5uuI8d545TLZMTjNjyvZXTx/8As1QhpFfRkT0Ww4jsDaKn\nUKJZoaLj5eFdTMkwelUWkJppCcZiT9sQ5NbhzH1xlLiIl0x1bgTTZSI+lnyEBXkORXEhflOIQlSF\nKWlW6lpRa8KkJ8NqpE8L8zZcpbGYEwq7UcrZ+gRoi3M60FyrCXU01KWplNViV2I69ENThSJD0eS3\nHYdbslmM5K4ynMKBlTlMAkTcgqQSjshiiffUQxdlMXe9CXYD30I61wrt6ZCgDv5sYpvyLpSQP8bY\n+j3z7FSpBFxpfDh2sUha/f2O43PGxBt3uX4xyOTyOtf1rMOnt2EegQ+Y9+3bQcUIqyy7CKr/AKt8\noN78Xvvfkbbf13xHVmddEloRy8w6sW5PuBYvbn177Ww1sHX1cI1U29FOCZt/IBIPv/j39OL8qN5i\nqjYDYlwem4VsOb/ntiGJPDVLobCzvJQiObk3ulYSL/hte+HcpyLoy5fVT4ZgD37CUQ/QR9Pbz24r\nxHFNy4a1E20LTfgXHvXO/wCI+O+KWbKcleXnYrSSClxtwBI32fSTt02N/n8ThpPpFnHmAe5jkL3/\nAN04l8efTfbYdvYeLyGw8Kkq33StQN9hcarbDr13+Hp49U3IM/KUMqIS82y0sd9J0EH5Ec/hxhyT\nclF8gY5h7dW9h/qiUQ/kPf8A6cCi2UMpUBY6k9/Q/PYdD/DDussuoqUNJBU5HdFh2Ox435Ox/DHi\nwlOuqJO39WGvUdl3/cO/mA69eLTCit9JcN7mxvxv6H/IfDC8pj7GyhOQzcLS4FgDY3UoJJv6X6fj\njQgp8FUDmEQEomAdAPgS6/Pe/wAvXuHHEhtLjzqUbi46bc7cWt136HBSjyAvK0RUkjWsLCtX/wBw\nkc9Rtbjrxh++0/8AfL+n/wDnil7Mr8kf0xBqif731/8A+sB9ZT7wm8feMHpodDrsHj9fmPYOC7Q2\nIVz+NgT1+nyxUdF1FSOQATsOxPfnjY/DCoqu0x7B43rx4ARAf4/qH58QLGly/wAevNiLj+Py6WxL\nHVdGwtfn+H/+vXnti0nLnzQROBomywc3yucqXMQ3np2JsjB7zE40nLnM1OVh2CzBujXJSBuNVVLX\nXpFfrM1U5Mj+FmXyaTp2n1EAvBmNPRDbWFU2lzwtaHAqfHcdU0tCSB5akPNkIIuVtK1IWoDUNsZ7\nmzJj+Zp0ORHztnnKBjxn4TreUKzGpzE9iS6l1apbMmnTk+1tlBRHnMlqRGbKkNqsb4IlT+kM5hYP\nmtnubyfWpOQ8iW2sz1BuNTuVVKbFtjxfYqujTHuLFKbAPoYIiitK00YRkLFw8i1WjisEHKrl84Xk\njyErVdnInqqq/JkSHW3GHmnmx7M7HcaDRjeS2UaWUtgISlJBTYG6iVXD1bwkyovJ8LIcRNTpNGhT\nIlUp8+nzj9uRK1EmqqLdcFRltSA/VFzVuvyH5DK0vF1aEttISylp4ov0gt0x/TbHjuKwNyyStA/p\nvdcw2G6ZbceWGywXLLlRyxRiyzOFUHt0IqaJbMWkf9Xq+Rl75XzyEYylXzF6sVwi46ZrT7LC2UQq\nepgTDPiNOMOOIp0rTpC4gL4OkAJs3ILzd0pWoKN7w1PwuptRrkOpSc050j1N3LCMp5hqUCrxIUvO\nlDS4t5cbMi26aU+e64t0rm0hFLmBp5xhl1pJQpC6v/SK5ZjOY/mT5h5zHGFL4PNvXpurZ3w9darY\npXD9wr839huDx6cUja21pixYyVfZSca9QtSjtB0s/SMdRFwmm35TXpaJ0+oLjw3zVEKanRHm3FRX\nW1lBKQnzQ4nSpAUkh0kEq6Gw8f8ACXL8jKGVsmx6xmOmHIExioZXzBTZ0NjMFPlxhJQHlPKgLhPh\n5iU4y80qClCkJaUAlSFFQ8jucixxuPMHYxmcW4NtONsB5uyxmmt0i8VuwzFVs8pmRMjeepF3j1bm\nzLL0WKbkTQqsfHuImeYqN2jl7PSrpoicKwqroaixFxoTsaFLlzW2X2nFtOqmCzjDyS8AthAADaUl\nDibAlxRAwWfyFAdqWYK/HruZ4FYzXl2g5Ym1OmTYcabBZy8SqHUqa8Kc4Y9TfXdU555MiK6FuNtR\nWEOKGJJc/pActv8AIPLndaJV8R4IrvKRNq2rAOKcXVmTjcX02yStiZ2W1Tsm0tllsdgtsze5Vi2T\ntsnYLIs5kmJCx7L7OL1qqXRV5BdpchpqLCZpjpMOLFQtEZha1Bbq1B11xx1x4geapxwlSRpTpFyQ\nMfwxoiKXnyiT5tdzNU87QkNZhrtbmMv1upRIsR2LAjNLgw4kSFGpra3PYmIkNKGnFFxzzTYDOwc8\ndtm5Hmqf1nDmCsVxXOVQa9RMpVbHNdt0bXYg8Hd/6Qn1spTOTucoeKtVrsx13NjVk1ZmEVQXOnHQ\nseuUrriKbWHVKrLLUWHHRU222n22G3UoCUviQXmgp5Wl11zdwq1Nm/uoTzj2ieG8L2Tw9kzK9mSs\ny8g1GXOpMyrS4L0t7z6eaU1AqDjVPZ86DAjAIhpaDElJSC9JdT7mEsxzz3W2YHp2C8pYb5fcxKYz\nqrrG+Ic05FpE89zhiOgOHovW1TqtvhLfCR0nFQS5lQqxLZBzp66g4XbtTrkOT4dlqqOyKaumyo8S\nR5MMtRJLzK1SmGvvhlLqXEBbbZuWtaVlAJAJBsKFW8PKZTMzJznl+s5loqqnXWanmOgUyosIy9Vq\npoDL1SkU9+E+7HlS0JSJ6okhhEpSUrWlCr3mth5xo/MrSkYImcXcu3KTy3WbPuNMlcwI8vGMrfHf\ntceAlW7B3bLQhI2e/WN8yp9WfWJap4/p5Y6EQlnoLNo1w4+rC3/RasmcpinuxKfTIEh5t6amBHdR\n5ykXSVuanH3FJabK/KYa0oSo7JJItPVfDxeXIFTzdHzBnDPecKXl6bTMrrzdWoEj7MZk2f8AYoPs\n8GlxUOz5jcQTqrUPOluMNaVOoRr1hnnIz4Tmi5ms75ybMPsaCvlxfOaTBC3bM/2dx3BIt6zjqAFo\n0Ii0aqx1MhoUjxBummkSTVfCUoioImFz6gqdWnZ2ny23pbiGmwAkNR0EMx27AAApZQ2CBYatVsO+\nScqoyj4Z5eyoHvapUGhJNQla1uGZWJYXUatM8xwrcWH6jIkFtSypXkIbBItiuUc56VSAbX9a3MQf\nYekA2PftsPx9eBclqwcWkbtyAra/VR4/yw5h4OQacysgrfjJTY7FRDZSoD/D441PAAke2OUB2R8H\ny0HxB7B6a1r5+oe3F6ErzH5oVwuKT0NzpHxtvhdzC2YqKEWrgMVFoGw4SoBZv/yd7bnbClF0BF3K\nXgVEAH12IAPbfbv5/LwIcVHGVJZjujgLKfTj+Hpx89sMq5TU2dKpxIJaYDxB5tqRyOg3B/IOM3HQ\noxZaHYpqn2HjWlAEvp6hv5eewb4mjOlszkkn9YlP4pt1+vqeDe+A9ap5k1rL8htPuxnHLkbgbNqH\nHHFh/PfGtUwEkQIHYASEfUO46Ht/EQ7D+PcddLQk05lfBLgGw42tv8/h88dUuorczhWYy1EtNxXL\nA3sLBKtgdtxfte/XG9usX4xxER8D2/IB9vAhruP4+d6puoU2pBAtcC21u/8AH5W74ZStmpU2Ywkh\nSQ6EKAsdwbkH83/nioIKip0D32Guw/gPb2+X/MeJYtg4Svix5/NvhfbjFGthUTLrDMYWIfbSANrB\nRVf7oO23x/lt+AP9oP0Hiz5rf7x+if8AqwqWmd1/n5YHKvSJjAO9dQgH47Ef8df48cJ5Jvaw7E7f\nL8/jhoNx7wOx5H87bfn0woSEADuPp7evn+/8B88QubkG3e3px3ucTtgWJHB/jv8A4fw6YPXL/gdv\nnWcnox9njl0wGxgW0MqpYeYjIz+hRUy7nn68bHRVYbw9XtkxPv01kDLTB0I1GOrscdGTmn7Roumc\nSkOCJwUlUyBCSgJuuc+phKitRSEt6W3VrNxddkhKBZS1JTbCTm/My8rNxn2ssZtzQ5KW+ExMp0hq\nqPx24rSXnX5q5E2DHitlKwmOlbqnZbwUzGacWlQFgq39GtzR2PmFzvywpxFGhcvcvFAeZNu8bZb2\nxg65I0lo7pxCWGs3N0zCvu4Z7B3iEuLeXm3NfjEqkWSkX7pm+YHiz2Wcv1JcybTdDKJUFkyHkuPB\nCFNAt2cbdIKChSH0OhSy2PK1KJBBSVur+MOSY+T8p53L9Tk0HNlUbotNeh0xyRMZqS26gVRJtOQ7\n7U3Iak0yVT3I8ZMp5U8stNIcacD4i+d+RnL+EZHA6UbP4uz5WeZwXDTBOROXS4Oci0XI9kj7JHU+\nYpsHLPoOsvRs8RZpeLinbJzGItjnfJLovDJovysuZNHkwlQ0hyPNaqIIhPwHTIYkOBwNLaQsobPm\nIcUlKgUgXULK2IHVF8SMv5qjZikGLXMr1DI5bXmek5tp6KTU6TCehvT41RkstSZjfsMmFHffbcQ8\npYDRStsFbRd6d1rkxvfKdyC/S1s7zfsDZAmUaByt1C2R+G8mscgy+IclV/mIj3tkxlkpkaKh31bt\n0cylGhjKMEpSAkTN5Nmym13sO/bIMLdJep1DzOh56E+4Gae04mJIS+uLIbnJU5HkJ0pLbqbi9tSD\nYgKJQoDGJniHTM7eLXgZKptLzRSYjtSzfOhO5hoztKj16lS8qvMRKzR3A/IamQH3G1gB1TMtsLZW\n5GS1IaWoCfQlMMYn5uMiWfNFcg7PjKgcs2TrBa4+xRrGUi28dP3bFGO1ZQ7eRavG6a8a3ujtyi6+\nECqAFVBJZD4iihamUmo32kuRKbQ5Hap0guhxKVpAW7GYKrKBF0hwkEC43Hrg7/aIl1oZGiUihS5M\nOtTc70aPTnIrzjLy1MU6u1ZLIU0tC1JcVT0JUm5SolJKVWANjvoluV6p4v8ApG+YWFzdW4a21nlg\nuC3LU1jbJHR8vDTGS8155YYJx45OxlWr5i+cDS2FytzEFEVDHQb/AFlE5BEq5SeWqe1FrVQZltod\nbgPiGhLiUqSp6XLENk2UkgqLQdcG3AuCL4TvHbOE+t+F2TKrl2bJgTc5UpWZH3YTzseQzTMu5eXm\nSqIDrDjbrbYnuQYTpCkjUrQQd0nlbhLlWcZ3tt0qrfPPLNhOQgMjjQIGPz/k99QpK6WiXnZqNhIS\nnxcVU7U6eoncx5I+QnZAkVXYaQeRrF9IkXftkzKMem/aEp0e20+GoOezoTNklhT7qlqQlLSEtOqU\nLpCVrVpbQooBVdQGPoCs51bybTYUleVs5Zjjyaf9sSHcq0RqqMU2AiLHkSpE95+dCbbUEvKdZitF\n+XIZbfdaZKWlqxponJJzAXrmAyxy2LQlapF2waa1SObrHkO2RtZxlh6tUd0i1st1vl9Ej6NY1Jso\n5ZHjZOPRkl7ASQYDDMnYLnFC83R5ypQjBDbLsVDyJ7jzqW40Vtg6XHn3rKQGhqFlJ1ly6dCTfZeq\nPiTlWNRkVxUqbU6ZmP7MeyrEpUB+bWa/LqyFOQqfSqXdt5yevQ4HmHlMJilp4SHG9I19LOXPlhXk\n+SX6UvCEDmzlstrSFyTyEzr/AJgozJwNeXeHqqU3cLNO2h1kew16Ik0I2BYKjGzDFnWHU4vYkjVq\nJipaTVQRWL02nlukV6O3Lp7iW5lGUqcmTpgoaDrjjizIcbQoBCV6VAIKy5+rSlSuc7zvnJK/ETwa\nrE7LecYC5WXPE2I1lV+i+ZmyROeiQoMWI3SIkuQypyS+yH47q5iIyIZEx9+OylakgHCvJznrAnPd\nTsGOKPywZyttkwZf8o4/Nkl9J3rlpyniyfw7cJ9hkmuyjKETk5M6MJGy8hSnC8G0VaW2LbFX+ptl\nG00mPj0adErCY6Y9Nmulh6Wx7UovU+RGeiOrTJQtKAokJQpTJKBZ5IuQCF4csw+JOVcx+GCa19q5\n2y1Aj1ynZfq32I2zTM5USuU+vU+K9RpTDsksMpcfejNVJtMlaXKfIc0+YsLjkQ4H+jqy3m3E+Ic3\noZV5b8TYryxdbPjCrW/OOWxoKSuSK7Jx0HGUJaOCuTEk+tN3dvVnNVawTeXZmi4mYk7E/gEWzUj+\ntBoMmoQjJ9ogx48x1bDL0uQWh7QytCA0tJbUrW6pd2tGsFKVFwosAo9nPxdoGU8zPZaVRs21qtZZ\njxKvUadl2iCpLVRahGkSXKgw4ZbDIi05tsImmSuKsPux2YrcpS1qbhNc5K81TuYc04JshqNi+Y5c\nP2llM+3nJttSgMW4kr9UlGkQ9sdlt0fHzSz6OlZCRi2tQa1uImpq4LyrBODiVxO4FrSjUma3UpkZ\nfkxlQmHTPfkuhEaK22oIUtx1IWVIWtSA0G0LW6VDQk3NjuYPEHKr+WMtZkhfaVcj5rl0wZTplGp5\nlV2vS5sd6Q1Dh0952Mlp6Oy0+uoLmSI0anJYdMp9ACPMGHMRy+X/AJacqpY/vqtalDS9JrGQKbca\nPNGstAyLju6sjyFSvtFsRmUcpMVuebIuQbquI6PfNXjR6xfsWzluYpp59PdgQmo8gsuKLjbzLrDn\nmsSI74KmX2HbJK23EkkakpUCCFAEb1skZxpuba5UavS0To7LcedTKhTqpF9hqtIrFMKGahSqnE8x\n5MebEeQA4lDzzS0LbdacWhacBVJYFG+gEdEWOHvrRv8Al+ncNhwHeZLTy07XU0g/UdfXf69cadS5\nTU+KiWLHRJfaB7aQng97W9N7DblUcpTPSn8iYuhD038MPA/p+fjXjjzzSYjbfGhQ7jhZuOeN+L32\nxSj04s1qsVCwBejKCT1P6gA/X+IOESBx2uYQ79W+3fQBsB1+e9a9gD34szEBT0dCQT+rO3G+38vw\n4scD8qTFtUSqyXybCYpQKr7CxT19fXoOu+FKCoaE3vsN/MB9v8j27/Kk4gocUm5Frgi/S3T5fx27\nFsQ41UaRFeJBQ4srF+PdUtNuTva/XnfDj8UPl/xB/hxHYev1P9cceyNf7v8A6f8ApwLz9zn2IiPU\nOvfex7fh/H19w4v8WsABc37W7/H8OnY4ooCtrbg/n436W/zwqT/cDfnXf8eIVAEnte46YtJFgPnf\n646Z8pOGqOlylcy3NtJYBb82mR8bZVw/g/HGDJkl/k6FCOsqRspJu8pZKqGL38LcbvGqOGbKjVKu\nBYIeAXsT1wrKqO1PqwNGOlxWRS59SXCFTeYkxYjENYeWygyUqUZMhqOpLrySQllpvzEIK1HVe4Aw\nzxCzHUnM/ZQyIzmhWRaNV6JXsyVjMsf7LZqklqiussIolIn1pqRT6c8lDjlSny/ZZEpMVtIZCE6y\nvsrmgkq258fpYyTEO0rc2n9B0qSVgoxFVoxhJIMRYPRkYhkio5drIs41wC8a3SVdujptkCIKOFxK\nY52eVqFczNrQG1fogNaEghKVCLDCkgEnZO6RcnYWJO5x8/0HyHPCbwLEaQuWwf7Sn93lPKStyQya\n7mUsvuKCG0qcdTodWpLaAVrKkpRfSKw8qlnrNRw79ApZLo6aM65FfSH81BX8hJLpt2EYrI3OpxEP\nIOnKwlRbNWNhkol6qsoYiSIpfHUMUCGOFCnLbajZLW6UhpNcqV1KNkp1OtJQok8BLqknfYW7Yb84\nRZtRq/8AajiwW1uTXfCfIvltMoK3XUsQJ70lptCbla3IjL7YSkFSgdIBJsYhXMGZuxNyl/T1L5Zp\nFwrHXaMPVgZmzRMnFMrXZY7m7lLLKvq87kUEEbOx+xrJBzis5DnfxhGdnh1DvSnlkCKRsxJcSn5z\nVKZdbu7Fb1OIUlLqxU1LWWyoAOp0OIWXE3QA4m6gVC96p5ky3mHOP9l5ugVOnzVohV+Z7PCfYfdg\nRFZFjRo7UtDSlKhu+0wpMVMeQGni5CkANn2dWmlHI2LiPwj9KTY26hkF2fIBI1hu7KJinbu73zA4\nei2p01ChtNT4kaJimLo3UmBgMXpEwCaQopgZkIJBRSFISf3S9MioBBtcG6QRv06WvjQ/EyK27nDw\nTbWAUy/EtmS6gjUFppuWK68u6TsRpeIN+irEEc9qbbkyppZc+jZzNW5OPGxfSZc7vJDzS5PaxgGb\nqxiWBcZ48wXZImSRDZR+0c83e+2FQAExF3jNRYehf4xEmx2U0JVAlNqT5mYarSahIAuClMKOxDWh\nQv8AtTH3l9blJJ3vj52p+Xp6qB4y5dmsPex+DHh74i5PoanSFh5zM9ZqeZYshomxHl5ZpdNii4BC\nHQjdJSTR+G5eavjKqZ05hIrlsi+bnNUz9KJkvlLpWOLYxyDYscYhYwdlk7S2utlpWM52tytmttxl\nXaERUhtMq2p8G0YhJqIOXgLpLBI8BphMmeIKalLVmSVSmWHQ+uPEShxbnnLajrQpx15RCWvNUGkA\naiCrGl1PN0+sP5fyqvNzuRsvxfBGiZ+qFUguUqLV8wvSIceEabDqFXjS2YcGnx0LkTvYWVVCS455\nOpDekptrzNV+QyNl7/tEGHsbQ76w5utL3lPv8FU4GPWk7ZcMUYrlqlL5diK5FtE1ZCWUjyScHNyU\nZHIrun7YrdJNBwouikqaqiVyTnSFHQpcsvU99DSElTrsZlbDklLaR7yyAUrUlIJIAAFyAc3yM5Fo\ncf8AsrZprD7UTLzcHONIlVCU6liBArdTaqkWiPS33ClpgOlL0dp51aG2lFSlKQlKlJ5sYFh5+s/R\ne/SgxVih52vS5ct/R7ndxVhipSClU276+3J+yVdRku2ZSCSTxqs2fNDuGxCOW6rZ2gKiSiShl6E2\n4nLOY21pW2tEikLKVpUhX+uWsXQsJULgAgm1xYi4scbVnKZEe8cvAydDkRZcZ6jeI8YPxJDMlhSk\nQ40Z1KHo63GlKbWtTTgSslC0rbXpUFAdOcK9Q86n0OBzCJhD6F60EER2JtFxLzGgUNjsekoF6Sh4\nKAABew64ZIBvUMvpO5OUQQe5DU8bfI9uoxiWcGiMk+Nq0gAI/tJKQoAWA11PKahwLbqT3359cctb\nyKg/RVfRqAUxg6OcvmcU7GMACckhj8oH12ATFBRQpTa6gAxwAQAxgFYB8vLlCTuNdQqg7XN4xvvf\nm3TG7qZ9o8cvF5YAKmck5DcHBslLdXuD2/ZKhvewJF+OuuV56LNzE/8AaBaRG4TrHMZkZzMcqGTY\nvCFlC/HSv+N8ZOqw7yMsyZ4vna1eZVxRFpuAu54yElkwcKs2ij1pIIgRoq1TtAlZwSiG1PfcVT3h\nDc879fHirbMggR1tPLLPmIeKEL3KRqBGx+e8qCQqi/2ZZcjM07J9Hixs40dzMsM0oKpNXrseoIpK\nXHK3Fm0thFVEWTTA/JjkoS6sNLZUS4ngNzfZ+ueeLBhZra8F1fl7i8MYOicUY3oVWi8mxjImN29k\nsVjgXhv6WJmdtUi2K+mJdpFyJn6zBdokoRBRZRJUwIlTqLstqE07CbgIhtssMMMpkJAjJdWps/3p\nbjqgVLWAvUUqANr4+q8jZJp+W5GZ6hAzPNzc/mKozavV6vNfozzqqw/Baiy2v/YMeLAaXoZjreZD\nKHULWCtKQpN6XtjmTYrGMP8A/IU9+2xDQ7EB86/X29fJLKXZ6UpBt7Om4A7Dg7+v5AwTodTcgZWW\n64SFKqjgTqt+2lO255sD+O/GHUpxBRI2w3r/APrr19g/kOuA5QdChbYH16KuLfTj69cacl1ClJRc\napEdKrdSC0Dt3O5sLdLX6nESj0L9OgExN/n1B7/j/H8+LCXNUllSr7H+X06b/XC9Ngey5cqEZkaV\nLIV7vJKnBvwN+p9NrHcY07FJAB8D1CGg/AP013+foA+OJAkPynO1gbjpt+P0N+2I1S1UfLNMSu+q\n+gj3rlRUVdr8H4DCj4o+/wDEn+PHnkj0+px59sn0+pxCR0Jh9uof5+/EBJuodzv8r2+X+GDyUABN\ntwbXsP4/j8MbdlD1D9Q4j06jc+ot8zb8Pxx1q0ggX5vc9Nhf539MWCwnK80lKrGY8qcvFkzNR6jS\n63XYnOl3xNcLDTY+Hqd5nFK/WY69v69NRDlzE2CwCtGxKCib0CyJlRR+qCoosctCVUGWZUiE5KZb\nabQmW7HdW0ENvLKG0vFC0EpWu4SCFe9fjfCLmdnJVTn0Ci5riZeqc6oy5b+WqbXIESoPSJ1OjiTM\ndpjUuM+hD8WLpdfUFNXaCQrzAkJEQVzZmRaRnZpfLWSl5m0Y/bYns0qvebKtJ2PFrOPYRLTG08/U\nkju5eiNoqLjI1CpyCriDSYRzFqVkCDVEhKntUouLWZMnU6yIzii+4VLjhIQI61FV1MhKUpDSroAS\nkBNkpANpy3l5MKNHTQaMmPAqa67CjppkJLMStuPPPuViK0lkIj1Rb7zzyp7IRJLjrq/M1OKJjr68\nXOWqNdoUnbrLJUWoSU9M1OmPp2Td1WsS9qM2Us0pXoBZ0eKhpGwqM2ak49jmzdzKnatjvlFzIJiX\nlb7ykNsrccLLKlrbaK1lptThHmLbbJ0oU5Ya1JAK7DUTYWmiUynNSqlUmIMJmpVKNGjz6i1FZRNm\nMQQsQmZcpCA/JaiBxwRm3VrQwFuBtKQogkO18zPMbkCNdw19z9mq7RLyoR+P3sVb8pXeyRjyiREu\nxn4ynO2ExOPGrqtMJ6MjZxvEuElGgS8cwkjpqPWTVdK2/NnvkIenTHW3GksFLsl5aS0lSXEtELUo\nFCVoSsJ3GpIUfeAIXKRlXKNLZVIp2VsuU6VEqb1UTIg0SmxH26i+w7EfqKHY8ZtxEx2I89GW+hQX\n5DzrIIbccSodwl0ttch7VA161WGCgr5Fs4G8wsRNSMbFXODjZdvPR8Nao9m4Sa2CKYzbNpNM4+US\ndNW0o1bSCKRHaKapaiHHWxIbQ44hD6NDyErKUOoCgtKHACAtIWkLCVXAWNQFxcMkqFAmu0qXKhQ5\nUmmPuSqXJfjNPP0+S6wqM7IguuIUuK+7GccjuOslC1MrWyo6FKSZzQV835BuGNahjJbKd2vtRWUL\nhmsUle12S1VZzHyj6/LkxpDQ6juSgVWUyjJ3RYKy3ZghKEfWFTpeAs647ZEx92I3H9peeaUoRW2S\n6440QVPn2dKblFlhTp8tKbKCnDY3VgfV/wBGaRCr9QrCKJTqXPQk5imVJEKJCmodZZpiPtmQ+EMy\nw7HUzTk+2LWVslqILoKUY3QfMLnuoL5FGq5ty9VVsxkkS5cGv5GuUAtkxaRXfKyhsgDHS7Na0uny\n8jJfaC84Ll44M/kUXCpyPHaSs8eVNaRJU3Lktl50mUUPuoMhKiVK8/SpJcKiVlRXcnUq53VcTU8t\n5VqEqiRZ+XMvzmqZDCcvmVSKfKTRvIbQiP8AZXmx3EwUtIaZ8lMbQ2gNNKQlJbbUltjs15iaZEQz\nO2yzkprmJF6R8XKra9Wdtkcr5COQiEXQ3VCTTsRliRDVrFAY8gcp4xshHqFOzTIiHUiXJRNXKbkS\nEvrCHBIQ84l/UEBIV5oUHNkgJNlfdAB2FsVqHl2hy8stZel0SkvUeM/Iiqoz9OiOUtTSn1vls09x\npUVSS66p63lXDqi6khw6istue84ZBG7q3nM2Urkrk2Uq8nk0bRf7PO/0hSNITFGlPrsWSk3BLO5p\n6IijVVZcroa8iPwYf6mlonEy5ctS5QfkyHRNabW6XXnF+cpoWbU5qUdZaBIb1fcGybDFKFl3LzSK\nP9l0Gj045VqMuPS0QKbEippceoOBc9uCGWUeyInLGuYlgo9qXdb/AJirnHzPN+ZY6VqNhi8uZLjr\nDj2prY6os2yvNlazFLx85aSUe4otVkkZMjuvU5wwmZdkvW4pZrDqtJWRbqNBReuCKQIlS2nG3DIf\nCkxCwwsPOBTTJBHktKCgUNgKUPLSQmy1C1lEE1Ky9l2pM1OCuh0dxmRX2K1VIyqbDUxUaolbbn2l\nPaUyUS5+thhQlSEuP62WlBeptJEdNfLo7q8BQnVws7ilUudk7JUKevPSatWq1gnxaGm56uQKjo0V\nCzEwZgxGUko5q3ePxZNBdLK/V0eiB1bwjxUea4WUeattorUW2nFlIWptF9KFqCRqUkArsLk2GDEO\nHTVV7MMwQISajLZgRps9MZlM2bEZQ6Y0WVKCPOkxo5dc8hl1a22vNXoSnWbyVLNmZGmVnmb2uW8m\nNsyKuyzR8tNr3Z2+SlJYWScaeRVvCMoSyLO1Y9BGPXWWkVBcsUiMnAKtSlS4somSlGLJ9pk+1h9Z\nVJ89wSCsgAqL2rzCSmySSrdIAN07YAu5cy+w3WaCqg0ZWWzRmW0UJdKhKooZacL4aTTFMGGhCXlK\ndQlLI0OqLiNKyVYS33K+S8yWg96y5ka8ZRub1i1YOrbkO2TlzsazFgRQrBgeYsD1++KwYkUWKxYJ\nrJsmYKrA2bpfFUA1ac7JfkPLlPvSXQtKS4+6t1zQknSnU4onSm50pBATewA3wbytTKJSMv06HQqT\nTKLAcQ44mDSIManxPPeUoPuiPEaabU88UjzHilTjmlGtZ0iw4cl6GRky6ETOOodD/aEe3z8B8x8c\nWoruuaVqJsGLfSw67dr22GF6vU0xsusx2uVVVlSgOytdySP47X743nWAHbVPYa+EAm/4PTx/kO/t\nxCGgYchzg+adJsf9p/Q/Q+uDKaitGZqTCKiE/Z6CQTexMXkjvcD4DfCkipTCqACAiAAGt+fXXoP9\n+td+4cU1tqQWlHYKBN/wvyfS/T0thmYlNTW5rQIIZcShQ7XCjufS29/hbnHxwA6YAAl/f2Ab9A7e\n/fwA9h7jvsO98SMOFpxxRBuU2v09DtuAPX03AFsUK/CE6FBYR91uQF2HbTY3AtxwOR8+FPSHuH/E\nH/y8fvOPr9BiP7Kb7n6J/riBb0Y+x8mEA/IRH+/jhYvwONz89v5YLhzSQOQR8vT+fp/EZcfkp4N/\nW38MQuO/eHUi4I/H473/AMeMdX+TIAH6Nf6Y8RABEKDySaEQ2If/AIl3e9D6fPXDLTP/ANCzR/8A\nYpP/APcDjBfEG/8Apg8AACReqeI3/wDh7XrvgD8qPLbj/JGOuYPmKzk8ycGDuXFpjqMlKphRrArZ\nZypkzLtgdQdEx9UpG0Rs1XasxbMouctdwtsrBzScTCRjdq0j1HsokshQp1PZfZnT5ZkeyQPISWog\nQZMiTJcKGWGlOBTbadKVuuurQsJQAEpuoWc895yqtGqOU8o5aboxzLnE1Z5mbmNySihUSjUCIiTV\nKpPahPRpc11bj8aBT4DMmMXpLy3HHg2wpKp3nDlp5dOWXmUp0FkaX5ib1yzZbwRj7mFw2egx+Oaz\nnuwwOXYP67SaTbSWxq+pkBOQ1hY2Gs3GVioWRcqmi2DyErZXEkqyZzz6fAgTmUyFTnoEmGxNi+QI\n7c1aJKAWWXfNCmkKS4HEOqShRukFCLqISEyhnLN+b8pVR6kMZSpmcqFmWqZXr32s7V5mV4j9DklF\nSqMEwXGqhKjvxXIsunx35LKAH3ESZhQylxyzsV9GLiW288XJpg+tXDNMHg7ndwTOZnpB8iQ1eruc\ncZPI+m5HeKUfIDb9nxrrtzBXGmxqcnMR9bahJ1mUcjHtyPUEJNckmgxnatSIjbstEOqxFS2S+hDc\ntghp8+S+PL0FSHGkhSw2NSFE2BAUUV3xgrkHw38Ssxy6fl2TmLw/zDGy7UhSn5crLdYS7UaSyKnS\n1e1e1tok0+ovLZYelrLMxhHmqLSlspiGP+UDkHvdV5wslxWbOZeTw/yWUnl8kbZcIqo45aWDMFzu\nGRLpQclNMbVeYIRtAVW3ykXUo/DMtbpVN1XEJaSn74zsDVBs0U5ZpNHfFUkJkz1RqaxBUtxDbGqS\n66+8y+GEKFkNuKS2IynFXRqUt5KxYYkqfiL4mUn9AKQ/QcpM17O9YzVHiwZEyrLj0Kn06lUypUld\nXlx1FcmZCZkTna+xCZKZRYZjU1cVxS1AyYZ5J8dMPpCvo+I/lpzxzEY6w/zmYanM1YzyK0lqvWOY\n/FAtKXk1ha6g6skDEGqryRbSVbCJcS7KDBlIwM7JMSpLnQRk17EWjMIrFE9gmTmItTYXKYfCm250\nazUgOMlaE+USFN6VLCNKkLUOQFERmLxOq73hn4rfpjlrKdWr+RqvHy/VaUtibMyjXCqpUZcKoNQ5\nUj25ttTExMlth2SXGZUVl0lIUplNZcPcsXJux5PqBzi81GQeY1GOsHNVkzl2f49wg0x45n54ISv1\n+yRFuZz98YKM6+yrca4s01eDvBsUpanAQEJWI6HcLyUmpDFplMbpqqhUHpgQ/OfiLZihnWoNtodS\n6hbwsjQlTindWsuEIShKSVEk8wZ6z5JzyjJuTqZldUilZVpOZGqnX1VNEZhyXNlQHoEmPT3krk+0\nvNw2IAaEVENJkvynX0oabTOpT6NjH+K+bfnSxxmbKFxT5ZeR+hx2Y77fKVDQpsoX6lXpnU3WH6PU\n2MogtVInIN9c3JlEOZOWajAxisRKPgYolds0WkbtDZZqlUYlyHfYKRGTJeeZSj2h9p7yjFZaCh5a\nH3i6ElShoSUqUQAQBbp/i5VKhkXItXy7RaaM3+JdcXRqXTKlIkiiUupU5U5rMFRnOMLTNfpVN+z3\nH0MsOe1PB9louqLbinAnzj8r3L9h3B3KTn7l5ueXbRUubFDO1kQiMvtKWysFGi8YXSuU5hUXxKW1\nLHyNkh5N/PR1isbZ4eEshWEXMQUXCN3azQ8Nahw2YdGmQlyVNzm5e0kNBxtLC20JbWWhpU4hRWla\nwooWAFJSkG2C/hZmbMtVzb4nZXzVEokaflSVl0OO0NU9cKbIqcWXLelxzUFF9uJIaTGeixnEiRFD\nrseQ8+pAWOdSJ/8ASXSY+Q6Dhv2Hf6d+/wD0HgM+n+7Q3Op1IJt8uevBONOpTpGYcxxVX0pEZ9PX\nZQF7evvjex32+G8BErlfzoSEN6+g+nv2D+PHJGqNHsAbLWn134+V/wCuLrKixWqu4T7jlPivb8XS\nLE8fx4+G2FZgA4KiA7/qh0Ou3Yg9vy2G/wAOIGyUraSejoNvTUAbg9T0/ji9KQHYkt8fefpbiQRY\nk/qVKTvzft/W+ESCgposg/tmEo78++t70Hfxrfbz7cXnWg47NWOUpCh2Ow/p1tbC1TJqosDK8dSj\nd2QWiNx/3x2+BChc4Xj0nIJR9DAP8/8AD5633Dim2pSFBf7zZH8P44aZbTcxtTJ3DElpahYbFOog\n79Og+PyxgZPb5I4f6qAAGu4+BD9dCIh49A337Thz+4qb4KnTf6p9eL2+GAioKlZqbm2OhqA2lPYE\nJULXt6C3Yd7Y0NTiH1k5gDQG2Aj47bAfI+O/fWhHx8+JZTQK4qE/uAEDvsTb6dfrgdl+c4zBzBMd\nUbJkgpJ7JUtPPrx8h1wqTUAUSn8dYD58eoCIfkOuwBvXjim40UvrQP2bcfAEX+l9/TqcNkCamRSo\nclah7+pV77H9Yocn0AI+nbDjxXsex+hwT8xH5A/6MQM4AImEPQTbD5dQ+POv8j54lvY2PBO30H8f\nwO3GKxClIBB32F973t+Hbn0xmHgNeNBrj24vbrziLSSnUTc9efh+fTHXz6O1nUL7yi/SbYAlMzYK\nw9e83UzlUYY4c57yrAYlq067oeapi6WdFGenQWFRSOg2XWqRkxfHTcPY9JciCbsq5GWihp+m1+Eq\nXDivS2aclgzJCIzayzLW84Na7/dQm+wJuUg2vfGEeKq59Kz74M5rZy9mbMFMy5Uc7uVhvK9El12d\nFbqeXY9OhKVFjadIekOWSXHWgpLbykFSmyknPlVlLPyy485v+San88GCMO5/y03wDnTBHMFh7mUY\no4SsU7RZKxRt1wZY8/QzFlDU6x2emuSLNms0VvEkk26Me/d9T5DdmmKcp7NUpLVXiRZkn2KZDmxZ\n49kcW0pwPQ3JqAlLLjjR2DlkhQCSbkWXs+NQ851TIHiNO8N8zV/K9COassZlyrX8nunMcONUmoj1\nOzLFytIddkT4cOopKVORip8sqU62geUqyflwyJkyN5g+adrnPnHxBcudxDk9NT+UPmSvPMXUMl46\no+QJOdaztgp1W5hJgJChU/JTelSViiK7NnkEY+rWSQsDZhOFfOzqL+w35CJtREuqRnasKZ5dLnvz\nmn2Gn1LC3Gm5qtTLT/klaULKrNuKWEr1HeHM9Ko0jKuSHct+H9dg+HRz+J+f8n0vKk+k1apUpiMu\nNFnTsrRi1VKhR1VFmI/LjBpTsyI1FW7G8tsJTa2hZ+xpA8+X0OVpybzc4xy66xDyvZoqGfM5PsxI\n2+EiskLI5tZvWNtyJan5JBwo4lZVnFV2en1G6dyjjRE5XjvoSXinTgk1LjorGVnpFSjyTFp8tqZL\nVKDiEvlMxKg6+6rUTrWlLa1keaNKkXSpJKNUMtVeX4a/2g6bRsi1mhCu5yy9UMsZZay+qBKdpCXc\nvONuQqRCaLaEpjsrflRYwUae4H48oNSGH0J5T8qOQKLWuQz6VulWK41iCt2S6fylNseVeWm46Pnr\nw6rHMS7nrG3qkS5XSez60HCmLLS6UWi5PHxog8dFSQH4nACmSWWqPXm3HW0OvNU1LLalJS495U4r\ncDaSQpehB1K0g2TudsbFn2hVOf4k+D8yHTpkmn02bnp6qzGIzzsWm+15RRFiLnPoSpqKmVKSGGFP\nFAde/Vo1LBGOhnK1nfCdZ5mvoHbLYcu40hIHD3Kjlet5amZS7V1nG4ysEkGY0Y+Cv7xaRBCoTD48\njH/U4yeOxeuSSLBRFAyT1qdVggTIaJ2VyqTHQiLTZAkKLyAlhajJsh43/VqIWkgLsTqSbWIJxrOW\nWcyTMpeP7cah1iRKr+dqOujMM06Wt2sxm0UDzJFMQGiqew2phwLdjeYhKm3EqVqbWE86bveqQ7+i\nbxFjVpcKw6yHGfSF53vEjRUJ2MWtzCnS2H4uMibW9ribk0u1rknJdUfHTS7ROOevk1WrVyqukqQg\nORJaVl6EyHUF/wC15S1M6k+aGlRQgOFu+oNqOwURpKtgSTpxrlHy/UEeNGbJ7kCW3S1eHOXYkeor\njOpgrqDOYVyXITcooDC5bTOp12OlZdbbstaEoKSenXMBnfAOZucz6U3BKWfMS1ilc6XLnyzVnEmd\n5e2MFcMIZfwZUMVW2Arltv8AFqPYuu1+wSzGeq8nYljqsYSZjDMXyYvFEWyhp+XDl1mvwxLjhmqw\nYLcaVrSqOZENqO4ltx5BUlCFkONqVchCk2O+2Mpo+W8z5d8L/B3M6su1h2peHOa83Ta5l5MN1quC\nh5lqVZhPS4tOfS2/IfjNuRJbUYBLj8eQHmyGgVioX0i1Lisa8iP0TlFishUXKBK/VOdBJ/c8aSru\nfocnNOc8Vx1PtqnYXkbEjZ4GBnFn1cbWpmyTiLE4iXErDKKxbhoqcbXGEs0fLkZLzUgtiqBTrCit\nor9qHmBtZSnzENqu2HAAhZSVJukgh68Kas/VPE3xwrj9LqFFEw5AcRBqzKI1RaYOXVmK7MjtPPiK\n/LjIRMMNbhfjIkJakAPJcA4wl2Vyqr6GSL79wDXkR/D/AKa7Lp96O011Q8pI+dySO3PQfW+NwQfJ\nrdQnjZuRS2Vk7WulLZJvfn3TuL/HphSYRMVRXtsyXfXuADr8ewd/4dh4iR7qkN/uvDY+qh+e+Cbu\nlceRNRy9SVAKvudKFKF+vS/ztzfG5A4ikTx99LQAO99gHx7j5/L+PDydLyyL+478Byk+vS3126Ys\n094P0yAhR3dg6dupLZB9dvSx57YSrbA7EgAGiKDoPUdAAhv0HXcd+R3xcYVqROUTcrbF/wAbkDts\nNr9uMLFVilmTlRtFwlqcsqt/uqbVuPid743orAY7regBM4BrvoA0Pr379v8AHXpw6yQiKOdaD05I\n034+O5/pi9S6oFyMxFavdjSWkgngW80G3bcC4/nhWQwbKoGtiAa36h5D2EfPFRSTZSeiVG/e97fx\nH4/RkZcbdMd/q+w3Ynkgovyfjew22PO2ExyiVBYCB942+3ft94B7a/TyPb+FtDmqQ0VbBIHToEnn\nng9xfvhckU/yaDUmGwQp5aVHoTqeB7ep6et+MYKmMk3RIHkRAvfuPfYj/PWvb046aSlx99ZsRYn0\n4t8h1/jitPU9AolHit3ClOhBA+IUQfrf4j44d+s3v/AP8OKlkdz+flhh1u91fT/DEK3o5/bqH8hE\nR/h7/lxCtNxccj+H5/ngg2sJJQf2hex6/A9/yPTPjzcpChyPqenz+HxxIFAXSRe4/P8Alj0AAR0I\nFH/3gAe3rre+/wDD38cem33rEk2t1sem3r1PPbnHqSBcb3sLWJ6d99x36j5492GtdIdIgIHLoOkw\nDrYCXwIDruAhr33x0lJur1427fDbj629cVX3dIQu/CrG97i+wPfY/m+NhAAAMXpKJBAAAogAkEvY\nekS+BKGg0GtbAPbj1W6QOOQfh0t062+uI4t0uubn3vfBvuDwq3bc/H449AP6wB0A9XYd+oh4EffQ\ndgHvr9OOju0oHobjrb5HY3/l64hTdM9Dib2cQtCrcak7/wAbj44zIIG862U49x767CPn03rY6/Pf\ncOPFC1vUJP12PPzv87d8dRXQtL45U2pbavUBQtcG/T88YyEgdIgAB+9vWg0I73332Ht6/LjpKveu\nbbp0nptpt+fycQOMgx0p3u3IDqN+PeSrY323vjPQbEdBsdbH17b9db18t6+Xvze4A7X+h3/r+b4s\nFIQ9IcAsHEt355Cjud7X975c4MWEL1iXH9zfS2acDsuYekuq7JRJqG4yhdcPuWUm8XYKsrTEXKiI\nO5RCWiSNHLZBk+Yv4Z2hJuhes1FUmp0iVOdYjvNPSYqZbZ1N+X57sdSFEgh1LjXvakgEBKgpBCyS\nCbYRM7Qq1WaZU6ZRMwu5bnNJizvbE0mBWUyYzSFB2A9DqCkNhh9S0OKfZW3IbWy35bgCnAoic0nN\nE95j1cZxMNjeq4Vw/gvHh8a4Tw5TZawWKJo9WdzLqyTbmStdpWVsFwt9qnnJpS0WmUTarSblFtpm\nkZJZZ1YnT1TpkZsMtxosS8eLHaK1pbQpZcWpS1nW6464vW44oDVsALXKhGU8nM5TyzXp7tUm12vZ\njArdfrdQajsPzpjEZqJGZZiREJjwYECI0mPDiNFzy0FZLh1JSirJDdTX4nkfq49999gHy7a7CHje\n9D68UVAIllu/EgH0N/8AE/54bGl+dl1MwEa1UZzfgnywvb/08cgdL43tx6mie/JkhD+Ah6/yH+7i\nN8aZS7XsHAb/ABIP1/ni/SnPaKBFKgSpymuJPcnS4nv0P5tj1MwkM3J/uG7D7lD/AJd+OnAFCSv9\n1SP/AFEA2/r/ABxBCeVHdoEU3GqLIBB66ELI2NvTr8OmFAlA6iZvPQbsI+QHx/HXf/I8QoUUodHG\ntKR+JI+v59CchhMl+A5a4jyHFegJ0g9PTnjbfthtERSRkD9wEywAHce/cQ147B38/l24Kps47CR+\n6yTa1/2Un+Q9NucZ875kGn5rk7gvVJKEEbXBdWB+H8jheRbpM0J5MdMoiA/+569/l+P4+OKbjN0y\nli9kuKAI53UBt8B26W6Xw0Rqj5b2XIale+/EaUvp/wBxext6i/xtfCgBAwHANdh9R9R7++g7+O+v\n47rlJSWyeoNj6Abfn/IHkSG5CZjQsUtrQFcbXuq2/O6ev+WJyAcCb0Ou/wAvHnx29vTz8uPUKKC5\nbqLH4G5/PrjiYw3KRCuPdZcKx24A4+X4C/bDroPYP0DiDF7QO5/D+mIKIfeP7iI6/wDMIh+mxD8P\n5+A3+pH0OO3RpUlQv8R6W2H53/h74KHy1v8Av/yHffHuOXlLQEr5AsTbY268duf4b8e7Dt8/HHoF\n7+gvb06/THK3SlxCibJXt6A22O/4/HuBjIA322Pgda/kHtx+FxZXr3/j8fz61lkrU8yTyCpPz+fQ\n27Y2l30hvz6/kPH48m3F9vhi1FN20qOxCVJPO2ki/wDI9euPijsRAfQREB/XXf39Pw8cdKFkp7KS\nLj58/wBfS/fFWMsrecSbBTLygf8AhPB37gj/AAvt6QNGUD1EomDe/bWx/XXHSveQ0R0UEm/UA3t+\nem3GKjai1MqbdzpW0X0/8puO17gX+nGNxTAIFH3HW/n3/wAPy/LjlSbKWP3QT222/kf54sNyErYj\nLuLOnSe17f0H+Yx8c2imH+zof5D/AJ/TjpCPeb/3r/539Li+3TEUuRoYnKB3Y0m3/iQq/wCfwvjX\n5c632Ubj2+YefxDz50H5BxOABGP7yJA6dLWJ7cgfjgMpXm1xPVuZRjfixIBPw6fnpuNr4Z0gHyic\nADuHoOu/zDsI+w/nx+F/MQ6Bw8i/foPh2uOOMTP2ECRT+ppcgAf+Fwgb/wAsYogP1Uqeu/wjl18v\nvfmIefQR9fHHT28pS+nnNnt1G1/hybfjipTNsvtRD940+Y3pPPD1u3Pytt8cbGw9BEEvUSG7D29x\n0I6D1H38+B9/HhqU+50S4nj10/httviajueQxSYJBGuJJuL9Eqc4+Xf/ABxuOX+vb+xSqd/y1/ER\n/PjxBPkSSf3kD53+vFr/AF74llJ0VaiKGyW2ZgsL8BNvz1N8bEFAMmBv/EOX9BDQef8AO968jxy+\n3pc02P8Aq0n589emx57X2xLS5gfiB5SrXmvtg8f94kDr22/NsYLpgZA5Q/11CiIePJhH/p5Ht34m\njuEOtrN/daUO/wCyALD8/HA+swEuUyZHQLl+ey4Rze7yifgPxxqEpgfIa2JU0O/ffp7fw32DiYEG\nG93W727kG2xv6enfA1xpYzTS0i4bh01tVtrApaWN/pv3x42WH4TpUfHxNBvYh6h6/P8Az68evsgu\nx2+SEb29bXv8fp3OOKNU1og1+a4o29qSlJPoFpFj6374WFVAEUzCIgJwD22Ox8e+/wDOxHimps+a\n8kbhJN9r/dF/684ZmqglNNpzyyNT6UEepUspHp6+vph52HuH6hxUwd1nsPx/riBmH7x+++4gH4dW\n/wBO38ePwFzYdfz+fxOPzzoCAeiRfueg3A/O3PbMDAIb9w8b878aH5+g/wB4Dx+4x6HkrZHXbrue\nOD8P6bXwXsUcvmes9DNp4OwnlnMSla+z/wBoi4vx7ar19g/aguQiwlzVuLkCxp5EGTwWCbsySjor\nRyZEpyIKmLbiw5ksq9liyZIRYOeQw49oCr6dflpVp1WNr2vY2vY4Wq/mvK+XmYxzDmGiUEyy57H9\nsVSHTTJ9n0ed7OJbzRe8oONh0thQQXEBRGtNzMT6PTn4EQMXkl5sTaHpMJeX/KBukR190dVv94RE\nAKUe4iIaDuG7X2LWLEfZVR52/ub99r8/q7/T5bHdePir4Zh1lz/SDkoe6Qv/AN5qR1G/MvoQbn+e\nMi/R88+ggOuSjmtHQHNouAcmjoqfdQR1XN6T/wDWDrRO3XrfHgolYNr0qo2//ZyOP/LxKfFjwzQh\nWnxAyWdyQBmakblW4sDL3JPHNz8MYh9Hzz6dex5KOa7RiFMUf6AcmgBgHq0YojXNGKPQfpEOw9Cm\nh+6bUpotXLaR9l1C6T/8G/cjfpo6fH8cUWvFXw3RNdc/T/JnlutpUVfpLSdIWm1wT7VzYja97Adx\nfZ/6Prn06uoeSnmu2IGKP/3BZNDet9v/ANuB3DpNsA8dI7/dNrz7Fq4AAplRsFA2MORb5fq9sfj4\nqeGyni7+n2TPfYcaVfMtJ2ubjf2oHc336/HbAYytgLPOBRg2+cMK5Xw44sf15Suo5Px/aaIedTiz\ntU5Q0OFkjI8JL7OM+Zg+K0FU7P621MuQgOERN+kQJUZ7+8xn43mtKLYfaW1r021aCtIB07Xte1xe\nwIx+o+caBWqYVUGu0itfZtRaTKNLqUSf7OmQXPJ88RXXC0HghflFdgsoXoJ0KAEhj7M4L/uAIee/\nb2/APPFdCLCOrqHCkjvyL+lhfbBuXNK3a4zc2VDQ4na2+hPT4/jY264yTPv4J/X4QlH/AIfG/wBA\n9flrjxabB5Hd3UBfpsf577jb8PIz4K6VKVbUinlpR26oUD8wdvlj0VdO0yehkTeo/P0/AAHiRDX9\n2cURuHk7DtdJuDe43OK8moD7ehtAjQ9Tnwod/ddvt36Df+mPgVAq6SXbRkzdt996N+v8fb0Dj0sl\nbDrhG4cRv2sQPoNx19D0EAqHkVSDCBshcOR7vTcO3H8enIxkKvS6QANa+Gcd+fcd9/Hb+X5cepa1\nRnz3cb+dyLbfC/zt8ceuTvKrVJSkgITDlXtYAbLA4+P12txhSRyitpRJVNUpAEomTUIoUBEoGADC\nQxgAwlEDAAiGymKbQlEBGHyrJWkdVJvb678d9/SxwVcnBxcd43BaakAEixGq6TyN+CDbqDvfCRJf\n4aSIDrZ1h9/Uwf535D9NXnI4W86bE6GE9L2skg8dRvxbnrhRh1ZUWn09rUdT1VcP/hLyTx+bm25w\n4AuA9YdvuiA7/j4328eNh7jxUDBSEG33ge/Qj5fAC/4YZl1hDypLeoHy3G1EX4PvEdALfW/O2PPi\nFFUTgPcUwAPG+wD/AA767/z468shsI3sFlRv8f42H+A4xCZiDNclba1RUtA8cIVYbEWNz0237YQj\n91oYgeTnKIh8hHY79fbft+QcWwNUkKNyEoIHrt/Dc9/kcLK1KYoD0ZBOqTKbWrfc3Wb/AFHOxBuf\nXHqyoh9VTAewAG/mAeewD69xDf699ceNNAiSs/tEgfO/W19r/nrJUZ7iTQ4barBsIKx6JWL3+l/j\n8MP3xh+f6BxQ8g/vD6HDf9sD94fjiHmMGzj7GH5BvfgPw4q6LEWv6kn+lufpa+Djrw0WJ5AueABb\n8/H15HhRHpAPcOwgGw9vy9h7hv39vSkEg/X1xXQ/ZCgCdxxcAH8n59CBj9Nv0EYz05yp/SE0qiWt\nrAZFmci8n8tEsUbpD0ywSdWgLm7k74jEupa747TcJPahH2GHXZq3KsMZkXZq+7n40kmK5NLyEttp\nFVC1oSpTkMgFSUkgIeSSAoi4B5I6+u2PhT+1+xMqEvIC48STJQzEzG04tmO68hDipNMWlKy2haUr\nKU6wk7lIKrWG3aq/4b5iLghlZzFZpLDScxfeYCRxKd7zUPfqdRx/kFljVpjGtS8ZW8mwST0tPdxe\nSn7uMRkxWYR1oRi4C3IuCNn0boXns9Hmv/MR/wBWPjH7JqW3/s2b0H/YZG9t/wDY9L2PU23G9sSG\nk1jmqjsi0Gw3DJ8HN1iDmOVFslXXvMzETEOBcOwJKVlyw5Jblt8I6km1yj7tecjVheqDPys1kejY\nx/pUqtnjCvTtf3nsf7Zr/wAxH9cfvsqpf/LZt9z/ANikfK36na3G/F9iL7Rv+jbnCJks1ljeYWPZ\nV5DMz17Zox1zKRi0XkCsS+YqW+sl0iIlOyLp0+NVxYhFpVCgIox6ME9xxbYIIiNRyQo7sH7z2f8A\nbNf+Yj/qx++yqiRtTZx9fYpHNh2a5vyfUHe22hWl850qTGk1H5uJW3ERS8Q1q71ma5na0uaVdR1R\nwHWMlSRnULcZtgpNoWekXS8Q06m6O6nmT+dZyZW8jeZBgX957O13Whfu4j+uP32VUTe1Om/KFINh\nubf6kW6c8Wv0GON/0+7xyw5Wfou6PZp5rJZLp9TywzyCxWt8Jb7AlPoVzE8dKzEzIQ1+yWR2EzNt\nJFyhKnt8wWQMcxjOG7oF4xgiZ2W2s0rQ4hZCphISpKiAUsAE2OwJBF+9+1sfXP8AZYhy4rXiCqRF\nkR0ONZZDa3o7zKFrafq61JQXEIClJStKlJT7yUqCiACCfzDCb+tOO9AZIA/T/H2/LhASPcQN9nb8\n9/r+e2Psdb2qdJUSbPQkoO56BIv69h6epxkB+lLz3IQ39/v6a/z4Dj3yrug72UpPA67X9T+H4bcC\nWGoQBVu1HXbuLBX0+ex4xqBQDLIKb7AkYP1Ef8h29d8WAjSy8ji7ieevHPyvf19cCFSy5U6bJ1cQ\n3Qo9gQ5fr3P4+mMDqj9cRMGgAEzB7a7HH+Gh9fX8+O0IHsrqTvdxJHw27+tu/pitKmE1+A7clKYb\nt9+4d/G3ffnBnwJC0e0ZkoMNkWSRjau/lFETFextilImZnitXKtOqtiSqDd7a2NVuFtJCVq1TFbj\npKciK/KSL2KYqPU0V20sNlpTiWnjpQt5JNwtQUoD9WhYbBXocc0oWtAKkoUpSRfcDczVOczCfn0x\nBclR6e9pKHY7brDCl6ZkqOZRRFclw4ZfkxGZDjbD0hptt1YQVJVc7m/bWy1o5lmrmawW+Rxw+xo2\ngsyWjF0JjJOVss7aLBUrjj+sqwbJELFievRykC3pzqwy1llG4UNexxcmxgrUqyc36kytxclTiVOF\nlTOl9TKWbqUtTbjSC2BrYSko8vWVqBaKwUpWUlRyJUo0OPQmYamYaKkzVzIo8aqSKl5cZiOzKhVG\nSmQ4r2arSHUyDLEZqK0sTkx3WnH4iXEyTJXInRHsfL26jWqTxhVKlXGrpzD3avWWx3GPlnLfNSxS\nZtB3YmcPjQ4TeHHdIg7rQ3F5xdlte2UW343bsEJiSrUfbVTWymQttRaT5AGlaVqWFf3gfrwpQDVi\nwW0ONFxl/WhxqwUUBej58npcokKZHRUZCqo6oOw3o8eG42k0c3o5Qwp6oI8qqJmPRZ6YdSpQjTYd\nQLhaalONbH6P6IlZ2UpTDKEqk5q+V7rjey5BWxNZE0Hc1B2flporSHa011e02rSEjp3OjmbTuX26\nm5mYKAsyy0KVGIjxH00VKlMshw/q1OoW75SrEpXGb06C4AAC+VBWq6koUdNkg45b8U5DMepVBcBt\nQlMQZUaEKnHuhp2NmCWp0y0wypxxbVJbYMUM6Wnn49nSXV4ZXn0ekzDUpnbLHllnDOjYddZkdQhc\nW3aXcOq39WqSbBxVDRLxzI2uPQn7UrXbk9CFhntG/ZuXsktDr1SQrkvK1lUUpaU4p4J/Vl7T5Liv\ndOi2jSSVgKUULIQktlKllJQUqUcb8VEPT0Q2KYp5Pt6KSHjVITQDwEnzPaA8hDcdwsx0yIiPNeTN\nElqO06iU2+y1T3PWNWGFsq27FjS1ObitSnTOKmJtepO6YQ88Zig8k2TCIezc84cxjH60gmynDPUk\n5ohju27Js3BIy9KRF9nfW0lRWUAJUoo8saiAVAJKlGw2AVeyuQAMNVFzIa3R489yOiGmSsvNMCWi\nZZlCylpa3kMsJS45pJWxoPk2AUtSr6Q+ZUBMQRHuAaAfbff8Pf5D6b1xCGyEqABsTuO/T8Px77YJ\nuTkreYdJ3bTZNzwSb7d7bdNrYcPih7k/h/8ALxx5H/F/zf44s/a//wBT8P8ADDIcdmNvf7w/l3Ht\nwECTcfj226X/AA+Pwxpzj2pNr9j87G3x73P03x56dh0Htv5f3/8AXjooF9jYdvz/AI4rpfGk3uCO\nQDsdv5jnb+WNJkkFTD8VBBYS7AorIpqiUDAG+j4hTdO9B1AUQAdBveg13a9tr224vyTiol9Ta3Sl\nZSHPesFFIJHPG199iSetucYg3Z9P/wCiZiId+zRv27eP/wAvyAdvQRD24k8oFQsAAbcgf06/Priq\nJ7vkOfrFkoUf21X5va+r8CBvta3GQt2eyj9TZaENaBo3+f8A4Xn+fbv449S0NKgQNj2HH8uP44ru\nTXA8yoOLstCkkFaubXt97e/4/DHhWzIA7MWIdx0Is23bv7Al7/z18uOyhKiBpSTYcgfu37YiRKW0\n2r9Y5bzFEfrF8Fe21+gPccfHGsG7Mvxf9CZ9hAQH6o3ENiADvXw/cd/3cTeWD5ew432Hc+m4Ft74\nHmY42mYfMXYqKr61g7gH97Ynjjn53UEIiQB+Eggj1gHUKKKaQnAv7vV8MpOoCiI66t9PUOu4jvwN\nhJuOm2wA7825/PTYeOyy43YrKvMTcAqKugHUm2/bn8cZioACA7761/1147+/8PTtKDbZPrv/ABF+\nwxWXJ9/Xcfd0fK/X+VwOeMazq7KoG+3wxHt7a/x7D/HXbVhtvdCiOVgfQjt063/pgbLmjypLYN7R\nlHnbcEf5bjtjAqmkSm33BMB3/D2+fgeJi3d1SbbFwW+I67nvtbjf0wNTKCIbDpPvNxVWN+Dv/Em2\n4/E41irsQUH0SH+/uG/G97D8vXiRLViUW5cHzO56X527nfFJ2ZdCJZO6Iit/Q6vpsRthzh5p7ByE\nVORwtgkId8ylmIvo+Ol2QPY50k9ai7iJlpIQ8o0BdBP6xGyrB7Gv0etq/ZuWiqyKnQbKXwQPuuJO\n6UkXSb7pUCki43BBB4IN94Vy0yKYtDhUUvQXm1aHFtLKHULSrS40tDjaiCqy2nEOINlIUFAEGe98\nzWWcm1tao291jxWFeOGT9clcwPgGgyn1iOcfWWnwLHj3F9VsrRD4wB9YZtJduxfpADd+3ctg+Fxb\nfceeS4F+UU+Yk+6xHQRYgj322kL2O1goA8G4thepUCm0t6E9G9uS+Irou/Wq1Ma0rSpKrxplRkRi\nbEhKiyVtq95BSo3wMWV4sMdTrFj9m9bpVG2TdTslgixioddR9N0RCca1B8SUXYKzDAYNtZp9Bq3j\nZBmzVSlXRHbdzpD4MKErS240D7jim1LTpAuWwsINzuNOtWwIHvG4wSkLjvT4U9YUqTCamMsOF1wB\nDcxTBkoLYWGl+cqO0pSloWu7aSFDe8BVBMW4kFNISqqiUwCUuhT6TlEgaDYF6DnKABoCgc4F0Bzb\nIttgug2FkM9u4Fuu25N7d979VaRKWiCpKVq1SagFGxN+Sb9OpG57b7gYK18zbkbJcbW63dJ5KUgq\nazjE4WPQhoSIbg6hahBUKMl5MkPHsSy880pFbgKoSbfFVkFYaKboOFlXCr107/OJW7GaSs3u4kJG\nlI+6kNpUQkC6vLShOo7lKd733hhLh06sS3ojRaV7K8XVl5103fdcluNoU4tZaZXLfekFlBDYddUU\ngJCUpF5HnS3E2gKAnECgHbQbDsABoCh33oNevjzxyYg84JA4Qm9h3HwO9rbW2F7dBi63XVCnuPKW\nSXJC9JJJ2skA78nt/mcbxd6MmX+0AD8h2HqI9/X+/wDGERtlm2wJ+e5442vxe/pi8ushK4qCsBSk\nouNt/dubb7c/jhz+s/P/AD/w8R+Sr82/rif7WH+0P1ONZgVExh6fJh8iX0EfQB9f8/JTCSfh3/O+\nPoBb9+FHjewte4+X5+Ax90qD/q67e4b8DvXft37B7ee/p+0m4B69PT+Hf6fC8C3kpB3JNr9bG3f6\nYxAqvfRQ9vIdh9fXv+e+JtOnpa4v8sUw/quSetuP4fm3bH3QcAMHT217l7DrQ+v+fz4kCSQk9R/C\n9x+f6YpLcF3Ugmygbj1t1+f53x4BTiBQ14Nrew323+XcPy9Ncd6d1evI/A/W+Kheulk9Unbm3Hz4\n/wAsYqAYAEOkd7Dv1BvXb8Q2PbevPgeJEIuRttY9t7dPS2+K0mTpbVYm4UD1tuoG+3y5xgYqnQcw\nhre/UB8AHz9PIcSITZSepH9Sf64pyZA8p0dVp3NttgBbgHp+NseAB9kDQ/u+4fx7/j+vp4GQN7Ls\nOCOvX+pFvnioZdixufebPf024436327YxN167FHYG15Dxsf972Dx3DiRLfvDsU9QD8/z3xTem2Qo\n3OzgG3/ER2B6d+x3ONQ9YmU7dujv3D+8R9w+e9Dv04nS1ZCNv2z1HPS31+mBz0kl6QOhYSm2/X5d\nev8AK2PDAcERAC7ACe5Q9QD3+f4a9N8Spbu6lXdzYfX+Y/POKUqVoguI3uGNItfb+e5v1698ajCb\n4Hgdin27h/Pfb+Xn8pktkv8AA/1hNjbkfh0t+O/Ua/LtTSi5v7KE335JF/X5349cfEE4JFLoddHj\nqDXoIf5/kPHSm/fUbAgrv2sL/n8jEDc20ZtkEn9RpPPUWHPoca9nBXsUfupD6l9/x86HXt+W+Jw1\n+rNx/wB4O3Hr8wL7fC+B7k3RJSRchEMgc9Sbdem3Tv8ADHwHPoPuj3Ae2w0G/wAxEd/9fTXQZNyB\nYWNrjrvYdsQiolSGzc7pUTyN9z/TjCcwmECh0iIAYR8l89h9/wC7iwhsgrI5Kd/699r/ANMDHpSV\nBgb2S6Vbgnext8eb3/phOb4gfHN09zAIAOw8CAdvPqH5b9OJkt3DSdrJIJ/j15wNcl2VUXRfUtBR\n12FtPy+XptjSb4gJok6ddRgEe4a8APjf/PiVLYDjiv8AdsPlfn6fDFJySRFhMAm3mFagL9bE8/Ej\nnrjITK/WA2A6IUB1svsHrsR8/n3HWvTkNANEW3USfxO3x2+u/U4lXPUuotkE6WW0ADf90dB3va/b\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image \n",
    "Image('../../../python_for_probability_statistics_and_machine_learning.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The features from a particular dataset that will ultimately prove important for\n",
    "machine learning can be difficult to know ahead of time.  This is especially\n",
    "true for problems that do not have a strong physical underpinning. The\n",
    "row-dimension of the input matrix ($X$) for fitting data in Scikit-learn is the\n",
    "number of samples and the column dimension is the number of features. There may\n",
    "be a large number of column dimensions in this matrix, and the purpose of\n",
    "dimensionality reduction is to somehow reduce these to only those columns that\n",
    "are important for the machine learning task.\n",
    "\n",
    "Fortunately, Scikit-learn provides some powerful tools to help uncover the most\n",
    "relevant features.  Principal Component Analysis (PCA) consists of taking\n",
    "the input $X$ matrix and (1) subtracting the mean, (2) computing the covariance\n",
    "matrix, and (3) computing the eigenvalue decomposition of the covariance\n",
    "matrix. For example, if $X$ has more columns than is practicable for a\n",
    "particular learning method, then PCA can reduce the number of columns to a more\n",
    "manageable number.  PCA is widely used in statistics and other areas beyond\n",
    "machine learning, so it is worth examining what it does in some detail. First,\n",
    "we need the decomposition module from Scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "2"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import decomposition\n",
    "import numpy as np\n",
    "pca = decomposition.PCA()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create some very simple data and apply PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e+00   4.44789028e-32   6.56191018e-33]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-1,1,30)\n",
    "X = np.c_[x,x+1,x+2] # stack as columns\n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Programming Tip.**\n",
    "\n",
    "The `np.c_` is a shorcut method for creating stacked column-wise arrays.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    " In this example, the columns are just constant offsets of the first\n",
    "column. The *explained variance ratio* is the percentage of the variance\n",
    "attributable to the transformed columns of `X`. You can think of this as the\n",
    "information that is relatively concentrated in each column of the transformed\n",
    "matrix `X`. [Figure](#fig:pca_001) shows the graph of this dominant\n",
    "transformed column in the bottom panel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lxOHDhzVdHrt27fJrzPTYsWM1XR55eXlISEgIQa2JwU00gLjHTLtDuqSkxK8x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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4326cbe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "fig,axs = subplots(2,1,sharex=True,sharey=True)\n",
    "ax = axs[0]\n",
    "_=ax.plot(x,X[:,0],'-k',lw=3)\n",
    "_=ax.plot(x,X[:,1],'--k',lw=3)\n",
    "_=ax.plot(x,X[:,2],':k',lw=3)\n",
    "ax=axs[1]\n",
    "_=ax.plot(x,pca.fit_transform(X)[:,0],'-k',lw=3)\n",
    "#ax.tick_params(labelsize='x-large')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_001.png, width=500 frac=0.75]  The\n",
    "top panel shows the columns of the feature matrix and the bottom panel shows the\n",
    "dominant component that PCA has extracted.  <div id=\"fig:pca_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_001\"></div>\n",
    "\n",
    "<p>The top panel shows the columns of the feature matrix and the bottom panel\n",
    "shows the dominant component that PCA has extracted.</p>\n",
    "<img src=\"fig-machine_learning/pca_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " To make this more interesting, let's change the slope of each of the\n",
    "columns as\n",
    "in the following,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e+00   1.36443189e-32   1.71524927e-33   3.68262901e-34]\n"
     ]
    }
   ],
   "source": [
    "X = np.c_[x,2*x+1,3*x+2,x] # change slopes of columns\n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, changing the slope did not impact the explained variance\n",
    "ratio. Again, there is still only one dominant column. This means that PCA is\n",
    "invariant to both constant offsets and scale changes. This works for functions\n",
    "as well as simple lines,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e+00   3.63254364e-32   3.47777102e-33]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-1,1,30)\n",
    "X = np.c_[np.sin(2*np.pi*x),\n",
    "          2*np.sin(2*np.pi*x)+1,\n",
    "          3*np.sin(2*np.pi*x)+2] \n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, there is only one dominant column, which is shown in the\n",
    "bottom panel of [Figure](#fig:pca_002). The top panel shows the individual\n",
    "columns of the feature matrix. To sum up, PCA is able to identify and eliminate\n",
    "features that are merely linear transformations of existing features. This also\n",
    "works when there is additive noise in the features, although more samples are\n",
    "needed to separate the uncorrelated noise from between features.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_002.png, width=500 frac=0.85] The top\n",
    "panel shows the columns of the feature matrix and the bottom panel shows the\n",
    "dominant component that PCA has computed. <div id=\"fig:pca_002\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_002\"></div>\n",
    "\n",
    "<p>The top panel shows the columns of the feature matrix and the bottom panel\n",
    "shows the dominant component that PCA has computed.</p>\n",
    "<img src=\"fig-machine_learning/pca_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [
    {
     "data": {
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06bnLCAsLM/VpCPVZTHIAoABYDuC7p+xTGv9/wV2jjKYn5VllZzYrPXjw4LnfoAMHDrB5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\nouTObQgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4325cd810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs = subplots(2,1,sharex=True,sharey=True)\n",
    "ax = axs[0]\n",
    "_=ax.plot(x,X[:,0],'-k')\n",
    "_=ax.plot(x,X[:,1],'--k')\n",
    "_=ax.plot(x,X[:,2],':k')\n",
    "ax=axs[1]\n",
    "_=ax.axis(xmin=-1,xmax=1)\n",
    "_=ax.plot(x,pca.fit_transform(X)[:,0],'-k')\n",
    "# ax.tick_params(labelsize='x-large')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/oZTqyf/2XelyCHEtMZlM5lKXQQixtJaihv44cN+Cbb8P7NJarwZ25W8LIS4Ti8UiAV2I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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa432490190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(1,2,sharey=True)\n",
    "fig.set_size_inches((8,5))\n",
    "ax=axs[0]\n",
    "ax.set_aspect(1/1.6)\n",
    "_=ax.axis(xmin=-2,xmax=12)\n",
    "x1 = np.arange(0, 10, .01/1.2)\n",
    "x2 = x1+ np.random.normal(loc=0, scale=1, size=len(x1))\n",
    "X = np.c_[(x1, x2)]\n",
    "good = (x1>5) | (x2>5) \n",
    "bad = ~good\n",
    "_=ax.plot(x1[good],x2[good],'ow',alpha=.3)\n",
    "_=ax.plot(x1[bad],x2[bad],'ok',alpha=.3)\n",
    "_=ax.set_title(\"original data space\")\n",
    "_=ax.set_xlabel(\"x\")\n",
    "_=ax.set_ylabel(\"y\")\n",
    "\n",
    "_=pca.fit(X)\n",
    "Xx=pca.fit_transform(X)\n",
    "ax=axs[1]\n",
    "ax.set_aspect(1/1.6)\n",
    "_=ax.plot(Xx[good,0],Xx[good,1]*0,'ow',alpha=.3)\n",
    "_=ax.plot(Xx[bad,0],Xx[bad,1]*0,'ok',alpha=.3)\n",
    "_=ax.set_title(\"PCA-reduced data space\")\n",
    "_=ax.set_xlabel(r\"$\\hat{x}$\")\n",
    "_=ax.set_ylabel(r\"$\\hat{y}$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see how PCA can simplify machine learning tasks, consider\n",
    "[Figure](#fig:pca_003) wherein the two classes are separated along the diagonal.\n",
    "After PCA, the transformed data lie along a single axis where the two classes\n",
    "can be split using a one-dimensional interval, which greatly simplifies the\n",
    "classification task. The class identities are preserved under PCA because the\n",
    "principal component is along the same direction that the classes are separated.\n",
    "On the other hand, if the classes are separated along the direction\n",
    "*orthogonal* to the principal component, then the two classes become mixed\n",
    "under PCA and the classification task becomes much harder. Note that in both\n",
    "cases, the `explained_variance_ratio_` is the same because the explained\n",
    "variance ratio does not account for class membership.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_003.png, width=500 frac=0.85]  The\n",
    "left panel shows the original two-dimensional data space of two easily\n",
    "distinguishable classes and the right panel shows the reduced the data space\n",
    "transformed using PCA. Because the two classes are separated along the principal\n",
    "component discovered by PCA, the classes are  preserved under the\n",
    "transformation.  <div id=\"fig:pca_003\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_003\"></div>\n",
    "\n",
    "<p>The left panel shows the original two-dimensional data space of two easily\n",
    "distinguishable classes and the right panel shows the reduced the data space\n",
    "transformed using PCA. Because the two classes are separated along the principal\n",
    "component discovered by PCA, the classes are  preserved under the\n",
    "transformation.</p>\n",
    "<img src=\"fig-machine_learning/pca_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "9"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0misRrRA0MzK9DjLA8PAwhUIBn89HKBTi0KFD2Gw2otGoWQozmUyaVc8ymYxZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa437062410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig,axs=subplots(1,2,sharey=True)\n",
    "ax=axs[0]\n",
    "x1 = np.arange(0, 10, .01/1.2)\n",
    "x2 = x1+np.random.normal(loc=0, scale=1, size=len(x1))\n",
    "X = np.c_[(x1, x2)]\n",
    "good = x1>x2\n",
    "bad = ~good \n",
    "_=ax.plot(x1[good],x2[good],'ow',alpha=.3)\n",
    "_=ax.plot(x1[bad],x2[bad],'ok',alpha=.3)\n",
    "_=ax.set_title(\"original data space\")\n",
    "_=ax.set_xlabel(\"x\")\n",
    "_=ax.set_ylabel(\"y\")\n",
    "\n",
    "_=pca.fit(X)\n",
    "Xx=pca.fit_transform(X)\n",
    "ax=axs[1]\n",
    "_=ax.plot(Xx[good,0],Xx[good,1]*0,'ow',alpha=.3)\n",
    "_=ax.plot(Xx[bad,0],Xx[bad,1]*0,'ok',alpha=.3)\n",
    "_=ax.set_title(\"PCA-reduced data space\")\n",
    "_=ax.set_xlabel(r\"\\hat{x}\")\n",
    "_=ax.set_ylabel(r\"\\hat{y}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_004.png, width=500 frac=0.85]  As\n",
    "compared with [Figure](#fig:pca_003), the two classes differ along the\n",
    "coordinate direction that is orthogonal to the principal component. As a result,\n",
    "the two classes are no longer distinguishable after transformation. <div\n",
    "id=\"fig:pca_004\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_004\"></div>\n",
    "\n",
    "<p>As compared with [Figure](#fig:pca_003), the two classes differ along the\n",
    "coordinate direction that is orthogonal to the principal component. As a result,\n",
    "the two classes are no longer distinguishable after transformation.</p>\n",
    "<img src=\"fig-machine_learning/pca_004.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "PCA works by decomposing the covariance matrix of the data using the Singular\n",
    "Value Decomposition (SVD). This decomposition exists for all matrices and\n",
    "returns the following factorization for an arbitrary matrix $\\mathbf{A}$,\n",
    "\n",
    "$$\n",
    "\\mathbf{A} =  \\mathbf{U} \\mathbf{S}  \\mathbf{V}^T\n",
    "$$\n",
    "\n",
    " Because of the symmetry of the covariance matrix, $\\mathbf{U} =\n",
    "\\mathbf{V}$. The elements of the diagonal matrix $\\mathbf{S}$ are the singular\n",
    "values of $\\mathbf{A}$ whose squares are the eigenvalues of $\\mathbf{A}^T\n",
    "\\mathbf{A}$. The eigenvector matrix $\\mathbf{U}$ is orthogonal: $\\mathbf{U}^T\n",
    "\\mathbf{U} =\\mathbf{I}$. The singular values are in decreasing order so that\n",
    "the first column of $\\mathbf{U}$ is the axis corresponding to the largest\n",
    "singular value. This is the first dominant column that PCA identifies. The\n",
    "entries of the covariance matrix are of the form $\\mathbb{E}(x_i x_j)$ where\n",
    "$x_i$ and $x_j$ are different features [^covariance]. This means that the\n",
    "covariance matrix is filled with entries that attempt to uncover mutually\n",
    "correlated relationships between all pairs of columns of the feature matrix.\n",
    "Once these have been tabulated in the covariance matrix, the SVD finds optimal\n",
    "orthogonal transformations to align the components along the directions most\n",
    "strongly associated with these correlated relationships. Simultaneously,\n",
    "because orthogonal matrices have columns of unit-length, the SVD collects the\n",
    "absolute squared lengths of these components into the $\\mathbf{S}$ matrix.  In\n",
    "our example above in [Figure](#fig:pca_003), the two feature vectors were\n",
    "obviously correlated along the\n",
    "diagonal, meaning that PCA selected that diagonal direction as the principal\n",
    "component.\n",
    "\n",
    "[^covariance]: Note that these entries are constructed from the data\n",
    "using an estimator of the covariance matrix because we do not have\n",
    "the full probability densities at hand.\n",
    "\n",
    "We have seen that PCA is a powerful dimension reduction method that is\n",
    "invariant to linear transformations of the original feature space. However,\n",
    "this method performs poorly with transformations that are nonlinear. In that\n",
    "case, there are a wide range of extensions to PCA, such as Kernel PCA, that are\n",
    "available in Scikit-learn, which allow for embedding parameterized\n",
    "non-linearities into the PCA at the risk of overfitting.\n",
    "\n",
    "## Independent Component Analysis\n",
    "\n",
    "Independent Component Analysis (ICA) via the `FastICA` algorithm is also\n",
    "available in Scikit-learn. This method is fundamentally different from PCA\n",
    "in that it is the small differences between components that are emphasized,\n",
    "not the large principal components.  This method is adopted from signal\n",
    "processing.  Consider a matrix of signals ($\\mathbf{X}$) where the rows are\n",
    "the samples and the columns are the different signals. For example, these\n",
    "could be EKG signals from multiple leads on a single patient. The analysis\n",
    "starts with the following model,\n",
    "\n",
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"eq:ICA\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\mathbf{X} =  \\mathbf{S}\\mathbf{A}^T\n",
    "\\label{eq:ICA} \\tag{1}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    " In other words, the observed signal matrix is an unknown mixture\n",
    "($\\mathbf{A}$) of some set of conformable, independent random sources\n",
    "$\\mathbf{S}$,\n",
    "\n",
    "$$\n",
    "\\mathbf{S}=\\left[ \\mathbf{s}_1(t),\\mathbf{s}_2(t),\\ldots,\\mathbf{s}_n(t)\\right]\n",
    "$$\n",
    "\n",
    " The distribution on the random sources is otherwise unknown, except\n",
    "there can be at most one Gaussian source, otherwise, the mixing matrix\n",
    "$\\mathbf{A}$ cannot be identified because of technical reasons.  The problem in\n",
    "ICA is to find $\\mathbf{A}$ in Equation [eq:ICA](#eq:ICA) and thereby un-mix the\n",
    "$s_i(t)$ signals, but this cannot be solved without a strategy to reduce the\n",
    "inherent arbitrariness in this formulation.\n",
    "\n",
    "To make this concrete, let us simulate the situation with the following code,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "11"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import matrix, c_, sin, cos, pi\n",
    "t = np.linspace(0,1,250)\n",
    "s1 = sin(2*pi*t*6)\n",
    "s2 =np.maximum(cos(2*pi*t*3),0.3)\n",
    "s2 = s2 - s2.mean()\n",
    "s3 = np.random.randn(len(t))*.1\n",
    "\n",
    "# normalize columns\n",
    "s1=s1/np.linalg.norm(s1)\n",
    "s2=s2/np.linalg.norm(s2)\n",
    "s3=s3/np.linalg.norm(s3)\n",
    "S =c_[s1,s2,s3] # stack as columns\n",
    "\n",
    "# mixing matrix\n",
    "A = matrix([[  1,  1,1],\n",
    "            [0.5, -1,3],\n",
    "            [0.1, -2,8]])\n",
    "X= S*A.T # do mixing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "12"
    }
   },
   "outputs": [
    {
     "data": {
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hBYzW5ldKr8oBfdMpkbZQM8yKwBjVzI5FIsLttDA7AqO3bSVRJ8C44mWOMpjjZinGgoIC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\nXngB06ZN8/VZiZJ4+/TpYxs7CHZg/MECRoNu6nThU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b6Q4cQ/v7/bKillo5TyYwBbER8A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\nDMMwDJN3/A+n4LbT+Dl32QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4322abe50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(3,2,sharex=True)\n",
    "fig.set_size_inches((8,8))\n",
    "X = np.array(X)\n",
    "\n",
    "_=axs[0,1].plot(t,-X[:,0],'k-')\n",
    "_=axs[1,1].plot(t,-X[:,1],'k-')\n",
    "_=axs[2,1].plot(t,-X[:,2],'k-')\n",
    "_=axs[0,0].plot(t,s1,'k-')\n",
    "_=axs[1,0].plot(t,s2,'k-')\n",
    "_=axs[2,0].plot(t,s3,'k-')\n",
    "\n",
    "_=axs[2,0].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[2,1].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[0,0].set_ylabel('$s_1(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,0].set_ylabel('$s_2(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,0].set_ylabel('$s_3(t)$        ',fontsize=18,rotation='horizontal')\n",
    "for ax in axs.flatten():\n",
    "    _=ax.yaxis.set_ticklabels('')\n",
    "\n",
    "_=axs[0,1].set_ylabel('        $X_1(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,1].set_ylabel('        $X_2(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,1].set_ylabel('        $X_3(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[0,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[1,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[2,1].yaxis.set_label_position(\"right\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_008.png, width=500 frac=0.85] The\n",
    "left column shows the original signals and the right column shows the mixed\n",
    "signals. The object of ICA is to recover the left column from the right. <div\n",
    "id=\"fig:pca_008\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_008\"></div>\n",
    "\n",
    "<p>The left column shows the original signals and the right column shows the\n",
    "mixed signals. The object of ICA is to recover the left column from the\n",
    "right.</p>\n",
    "<img src=\"fig-machine_learning/pca_008.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " The individual signals ($s_i(t)$) and their mixtures ($X_i(t)$) are\n",
    "shown in [Figure](#fig:pca_008). To recover the individual signals using ICA,\n",
    "we use the `FastICA` object and fit the parameters on the `X` matrix,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "13"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import FastICA\n",
    "ica = FastICA()\n",
    "# estimate unknown S matrix\n",
    "S_=ica.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of this estimation are shown in [Figure](#fig:pca_009),\n",
    "showing that ICA is able to recover the original signals from the observed\n",
    "mixture. Note that ICA is unable to distinguish the signs of the recovered\n",
    "signals or preserve the order of the input signals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "14"
    }
   },
   "outputs": [
    {
     "data": {
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TlNK1De+9BOD6jf/9GiGE3vj7KgBQShcBvAXgUaXl1YramwjgO3VhRuPRKh6C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa432045bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(3,2,sharex=True)\n",
    "fig.set_size_inches((8,8))\n",
    "X = np.array(X)\n",
    "\n",
    "_=axs[0,1].plot(t,-S_[:,2],'k-')\n",
    "_=axs[1,1].plot(t,-S_[:,1],'k-')\n",
    "_=axs[2,1].plot(t,-S_[:,0],'k-')\n",
    "_=axs[0,0].plot(t,s1,'k-')\n",
    "_=axs[1,0].plot(t,s2,'k-')\n",
    "_=axs[2,0].plot(t,s3,'k-')\n",
    "\n",
    "_=axs[2,0].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[2,1].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[0,0].set_ylabel('$s_1(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,0].set_ylabel('$s_2(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,0].set_ylabel('$s_3(t)$        ',fontsize=18,rotation='horizontal')\n",
    "for ax in axs.flatten():\n",
    "    _=ax.yaxis.set_ticklabels('')\n",
    "\n",
    "_=axs[0,1].set_ylabel('        $s_1^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,1].set_ylabel('        $s_2^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,1].set_ylabel('        $s_3^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[0,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[1,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[2,1].yaxis.set_label_position(\"right\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_009.png, width=500 frac=0.85] The\n",
    "left column shows the original signals and the right column shows the signals\n",
    "that ICA was able to recover. They match exactly, outside of a possible sign\n",
    "change. <div id=\"fig:pca_009\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_009\"></div>\n",
    "\n",
    "<p>The left column shows the original signals and the right column shows the\n",
    "signals that ICA was able to recover. They match exactly, outside of a possible\n",
    "sign change.</p>\n",
    "<img src=\"fig-machine_learning/pca_009.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "To develop some intuition as to how ICA accomplishes this feat, consider the\n",
    "following two-dimensional situation with two uniformly distributed independent\n",
    "variables, $u_x,u_y \\sim \\mathcal{U}[0,1]$. Suppose we apply the\n",
    "following orthogonal rotation matrix to these variables,\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "u_x^\\prime \\\\\\\n",
    "u_y^\\prime\n",
    "\\end{bmatrix}=\n",
    "\\begin{bmatrix}\n",
    "\\cos(\\phi) & -\\sin(\\phi) \\\\\\\n",
    "\\sin(\\phi) & \\cos(\\phi)\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "u_x \\\\\\\n",
    "u_y\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_005.png, width=500 frac=0.85] The\n",
    "left panel shows two classes labeled on the $u_x,u_y$ uniformly independent\n",
    "random variables. The right panel shows these random variables after a rotation,\n",
    "which removes their mutual independence and makes it hard to separate the two\n",
    "classes along the coordinate directions. <div id=\"fig:pca_005\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_005\"></div>\n",
    "\n",
    "<p>The left panel shows two classes labeled on the $u_x,u_y$ uniformly\n",
    "independent random variables. The right panel shows these random variables after\n",
    "a rotation, which removes their mutual independence and makes it hard to\n",
    "separate the two classes along the coordinate directions.</p>\n",
    "<img src=\"fig-machine_learning/pca_005.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " The so-rotated variables $u_x^\\prime,u_y^\\prime$ are no longer\n",
    "independent, as shown in [Figure](#fig:pca_005). Thus, one way to think about\n",
    "ICA is as a search through orthogonal matrices so that the independence is\n",
    "restored. This is where the prohibition against Gaussian distributions arises.\n",
    "The two dimensional Gaussian distribution of independent variables is\n",
    "proportional the following,\n",
    "\n",
    "$$\n",
    "f(\\mathbf{x})\\propto\\exp(-\\frac{1}{2}\\mathbf{x}^T \\mathbf{x})\n",
    "$$\n",
    "\n",
    " Now, if we similarly rotated the $\\mathbf{x}$ vector as,\n",
    "\n",
    "$$\n",
    "\\mathbf{y} = \\mathbf{Q} \\mathbf{x}\n",
    "$$\n",
    "\n",
    " the resulting density for $\\mathbf{y}$ is obtained by plugging in\n",
    "the following,\n",
    "\n",
    "$$\n",
    "\\mathbf{x} = \\mathbf{Q}^T \\mathbf{y}\n",
    "$$\n",
    "\n",
    " because the inverse of an orthogonal matrix is its transpose, we\n",
    "obtain\n",
    "\n",
    "$$\n",
    "f(\\mathbf{y})\\propto\\exp(-\\frac{1}{2}\\mathbf{y}^T \\mathbf{Q}\\mathbf{Q}^T\n",
    "\\mathbf{y})=\\exp(-\\frac{1}{2}\\mathbf{y}^T \\mathbf{y})\n",
    "$$\n",
    "\n",
    " In other words, the transformation is lost on the $\\mathbf{y}$\n",
    " variable. This means that ICA cannot search over orthogonal transformations if\n",
    " it is blind to them, which explains the restriction of Gaussian random\n",
    " variables. Thus, ICA is a method that seeks to maximize the non-Gaussian-ness\n",
    " of the transformed random variables.  There are many methods to doing this,\n",
    " some of which involve cumulants and others that use the\n",
    "*negentropy*,\n",
    "\n",
    "$$\n",
    "\\mathcal{J}(Y) = \\mathcal{H}(Z)-\\mathcal{H}(Y)\n",
    "$$\n",
    "\n",
    " where $\\mathcal{H}(Z)$ is the information entropy of the\n",
    "Gaussian random variable $Z$ that has the same variance as $Y$. Further\n",
    "details would take us beyond our scope, but that is the outline of how\n",
    "the FastICA algorithm works.\n",
    "\n",
    "The implementation of this method in Scikit-learn includes two different ways\n",
    "of extracting more than one independent source component. The *deflation*\n",
    "method iteratively extracts one component at a time using a incremental\n",
    "normalization step. The *parallel* method also uses the single-component method\n",
    "but carries out normalization of all the components simultaneously, instead of\n",
    "for just the newly computed component.  Because ICA extracts\n",
    "independent components, a whitening step is used beforehand to balance the\n",
    "correlated components from the data matrix. Whereas PCA returns\n",
    "uncorrelated components along dimensions optimal for Gaussian random\n",
    "variables, ICA returns components that are as far from the Gaussian density\n",
    "as possible.\n",
    "\n",
    "The left panel on [Figure](#fig:pca_005) shows the orignal uniform random\n",
    "sources. The white and black colors distinguish between two classes. The right\n",
    "panel shows the mixture of these sources, which is what we observe as input\n",
    "features. The top row of [Figure](#fig:pca_006) shows the PCA (left) and ICA\n",
    "(right) transformed data spaces.  Notice that ICA is able to un-mix the two\n",
    "random sources whereas PCA transforms along the dominant diagonal. Because ICA\n",
    "is able to preserve the class membership, the data space can be reduced to two\n",
    "non-overlapping sections, as shown. However, PCA cannot achieve a similiar\n",
    "separation because the classes are mixed along the dominant diagonal that PCA\n",
    "favors as the main component in the decomposition.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_006.png, width=500 frac=0.85]  The\n",
    "panel on the top left shows two classes in a plane after a  rotation. The bottom\n",
    "left panel shows the result of dimensionality reduction using PCA, which causes\n",
    "mixing between the two classes. The top right panel shows the ICA transformed\n",
    "output and the lower right panel shows that, because ICA was able to un-rotate\n",
    "the data, the lower dimensional data maintains the separation between the\n",
    "classes. <div id=\"fig:pca_006\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_006\"></div>\n",
    "\n",
    "<p>The panel on the top left shows two classes in a plane after a  rotation. The\n",
    "bottom left panel shows the result of dimensionality reduction using PCA, which\n",
    "causes mixing between the two classes. The top right panel shows the ICA\n",
    "transformed output and the lower right panel shows that, because ICA was able to\n",
    "un-rotate the data, the lower dimensional data maintains the separation between\n",
    "the classes.</p>\n",
    "<img src=\"fig-machine_learning/pca_006.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "For a good principal component analysis treatment, see\n",
    "[[richert2013building]](#richert2013building),\n",
    "[[alpaydin2014introduction]](#alpaydin2014introduction),\n",
    "[[cuesta2013practical]](#cuesta2013practical), and\n",
    "[[izenman2008modern]](#izenman2008modern). Independent Component Analysis is\n",
    "discussed in more detail\n",
    "in [[hyvarinen2004independent]](#hyvarinen2004independent).\n",
    "\n",
    "<!-- #  *Learning from Data*, p. 263 -->\n",
    "<!-- #  *Building machine learning systems*, p.231 -->\n",
    "<!-- #  *Introduction to machine learning by Alpaydin*, p148 -->\n",
    "<!-- #  *Practical Data Analysis Cuesta*,p.143 -->\n",
    "<!-- #  *Modern Multivariate statistical techniques Izenman*, p.553, 558 -->\n",
    "<!-- #  *Independent Component Analysis Hyvarinen.pdf*, p.147 -->"
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